My local group and I had a lot of fun with the Corellian Conflict, and we are eager to revisit it once the new wave drops. While we enjoyed it immensely, nonetheless, it was the case that we had a blow-out campaign where Imperials got an immediate and big lead in the first week and then just continued to steamroll the Rebellion until they reached their 10-2 victory. I've done my best to follow lots of other anecdotal reports and experiences people have had with the CC, and it seems to be that this sort of situation wasn't entirely uncommon. After some reflection and discussion with my group, other local groups, and some online groups, I've got a list of possible issues and some house-rule solutions that might address some of these concerns. I'm very much interested in feedback, so if you played through the CC please do share your experiences by copying and pasting the survey below, adding your numeric response after each statement (1-5, or DK). You can elaborate on some of your reasons, but please do this below your copy-n-paste survey to make it easier to collect the data:
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SURVEY (feel free to copy and past this with your responses, and I'll try and track the results):

Response: Enter a numeric response (1-5) from the Likert-Scale below after each statement, or a DK for "Don't Know"

1. Strongly Disagree
2. Disagree
3. Neutral
4. Agree
5. Strongly Agree

(1) The Difficulty-to-Reward for the Rebel and Imperial special objectives (Hyperlane Raid & Show of Force) is even between the two factions' objectives:
(2) The "Show of Force" Imperial special objective is too hard for the Imperials:
(3) The "Hyperlane Raid" Rebel special objective is too hard for the Rebels:
(4) Fleets expand and grow too quickly in the Campaign:
(5) Limiting starting fleets to one-upgrade per ship is a good idea:
(6) When one side gains the momentum in the Campaign, it is too hard for the other side to swing it back:
(7) Fleets are often able to fully repair all of their damaged ships/squadrons after a game:
(8) Spynets, Repair Yards, and Skilled Spacers are roughly of equal value:
(9) The three Base Defense objectives (Fighter Wing, Planetary Ion Cannon, and Armed Station) are roughly of equal power:
(10) The nature of the campaign favors big, hard-to-kill ships over smaller but more fragile ships:

THANKS! Once I've collected general impressions, we can open further discussion, elaboration, and exploration of possible ways to mitigate whatever is commonly held to be an issue with overall balance/choice of the campaign.

I'll start, and as an example of what to do:

(1) The Difficulty-to-Reward for the Rebel and Imperial special objectives (Hyperlane Raid & Show of Force) is even between the two factions' objectives: 1
(2) The "Show of Force" Imperial special objective is too hard for the Imperials: 1
(3) The "Hyperlane Raid" Rebel special objective is too hard for the Rebels: 5
(4) Fleets expand and grow too quickly in the Campaign: 5
(5) Limiting starting fleets to one-upgrade per ship is a good idea: 3
(6) When one side gains the momentum in the Campaign, it is too hard for the other side to swing it back: 5
(7) Fleets are often able to fully repair all of their damaged ships/squadrons after a game: 5
(8) Spynets, Repair Yards, and Skilled Spacers are roughly of equal value: 1
(9) The three Base Defense objectives (Fighter Wing, Planetary Ion Cannon, and Armed Station) are roughly of equal power: 1
(10) The nature of the campaign favors big, hard-to-kill ships over smaller but more fragile ships: 5

(1) The Difficulty-to-Reward for the Rebel and Imperial special objectives (Hyperlane Raid & Show of Force) is even between the two factions' objectives: 4 I think the Imperials have a slight advantage, but it comes down what both sides are playing. A good defense can really help against the show of force.
(2) The "Show of Force" Imperial special objective is too hard for the Imperials: 2
(3) The "Hyperlane Raid" Rebel special objective is too hard for the Rebels: 2
(4) Fleets expand and grow too quickly in the Campaign: 5 In regular CC, we saw exponential growth in some fleets while others grew every little. By Turn 3, most fleets were getting close to their maximum fleet size.
(5) Limiting starting fleets to one-upgrade per ship is a good idea: 3 It hurts "Christmas tree" ships that load themselves up. It does help with developing the ships.
(6) When one side gains the momentum in the Campaign, it is too hard for the other side to swing it back: 4 While it is doable, once one side has developed fleets that are 40+ points larger than the opponent, it becomes a major uphill battle.
(7) Fleets are often able to fully repair all of their damaged ships/squadrons after a game: 5 That's the problem with CC. Once you hit about turn 3, scarred ships are rare.
(8) Spynets, Repair Yards, and Skilled Spacers are roughly of equal value: 1 Repair Yards or Bust. No point in taking the others unless it's a high refit point location.
(9) The three Base Defense objectives (Fighter Wing, Planetary Ion Cannon, and Armed Station) are roughly of equal power: 4 I played all 3 and enjoyed them, I think the Fighter wing could be beefed up a little by not making it count against you for points, but otherwise none of them are terrible.
(10) The nature of the campaign favors big, hard-to-kill ships over smaller but more fragile ships: 2 The campaign values cheap ships that take lots of upgrades. They're cheaper to repair so you can get upgrades and new stuff faster. In fact, I think the best value ship is likely the Mc30 Torpedo Loadout.

(1) The Difficulty-to-Reward for the Rebel and Imperial special objectives (Hyperlane Raid & Show of Force) is even between the two factions' objectives: 2
(2) The "Show of Force" Imperial special objective is too hard for the Imperials: 2
(3) The "Hyperlane Raid" Rebel special objective is too hard for the Rebels: 5
(4) Fleets expand and grow too quickly in the Campaign: 4
(5) Limiting starting fleets to one-upgrade per ship is a good idea: 4
(6) When one side gains the momentum in the Campaign, it is too hard for the other side to swing it back: 5
(7) Fleets are often able to fully repair all of their damaged ships/squadrons after a game: 3
(8) Spynets, Repair Yards, and Skilled Spacers are roughly of equal value: 1
(9) The three Base Defense objectives (Fighter Wing, Planetary Ion Cannon, and Armed Station) are roughly of equal power: 4
(10) The nature of the campaign favors big, hard-to-kill ships over smaller but more fragile ships: 2

(1) The Difficulty-to-Reward for the Rebel and Imperial special objectives (Hyperlane Raid & Show of Force) is even between the two factions' objectives: 1

(2) The "Show of Force" Imperial special objective is too hard for the Imperials: 1

(3) The "Hyperlane Raid" Rebel special objective is too hard for the Rebels: 5

(4) Fleets expand and grow too quickly in the Campaign: 3

(5) Limiting starting fleets to one-upgrade per ship is a good idea: 4

(6) When one side gains the momentum in the Campaign, it is too hard for the other side to swing it back: 5

(7) Fleets are often able to fully repair all of their damaged ships/squadrons after a game: 4

(8) Spynets, Repair Yards, and Skilled Spacers are roughly of equal value: 1

(9) The three Base Defense objectives (Fighter Wing, Planetary Ion Cannon, and Armed Station) are roughly of equal power: 2

(10) The nature of the campaign favors big, hard-to-kill ships over smaller but more fragile ships: 2

(1) The Difficulty-to-Reward for the Rebel and Imperial special objectives (Hyperlane Raid & Show of Force) is even between the two factions' objectives: 2
(2) The "Show of Force" Imperial special objective is too hard for the Imperials: 1
(3) The "Hyperlane Raid" Rebel special objective is too hard for the Rebels: 4
(4) Fleets expand and grow too quickly in the Campaign: 3
(5) Limiting starting fleets to one-upgrade per ship is a good idea: 3
(6) When one side gains the momentum in the Campaign, it is too hard for the other side to swing it back: 5
(7) Fleets are often able to fully repair all of their damaged ships/squadrons after a game: 4 - 1 if you are on the losing side of the campaign
(8) Spynets, Repair Yards, and Skilled Spacers are roughly of equal value: 1 - Repair Yards are primary
(9) The three Base Defense objectives (Fighter Wing, Planetary Ion Cannon, and Armed Station) are roughly of equal power: 2 - Planetary Ion Cannon was selected the most
(10) The nature of the campaign favors big, hard-to-kill ships over smaller but more fragile ships: 3

Thanks to all who have replied so far, I'll leave this up for a week then report on the collected results.

Something that's not mentioned but should be: Capturing an enemy base early in the campaign is equally powerful to capturing a base late in the game.

Answer: 1. More than any other issue, capturing an established enemy base during the first 2-3 turns of the game is extremely valuable and powerful.

(1) The Difficulty-to-Reward for the Rebel and Imperial special objectives (Hyperlane Raid & Show of Force) is even between the two factions' objectives: 3 -
(2) The "Show of Force" Imperial special objective is too hard for the Imperials: 2 - Not too hard, not an auto-win, but plays to the strengths of certain Imperial builds
(3) The "Hyperlane Raid" Rebel special objective is too hard for the Rebels: 4 - Imperials can deny the opponent from scoring easy points in this scenario by forcing the fight to wait until the end. Easy fix: First player gains the points of any ship within 2 range rulers of 2nd player's deployment zone at the end of the game.
(4) Fleets expand and grow too quickly in the Campaign: 3
(5) Limiting starting fleets to one-upgrade per ship is a good idea: 5 - this promotes coordinating unique upgrades between players at the start of the game.
(6) When one side gains the momentum in the Campaign, it is too hard for the other side to swing it back: 4 - This is a major issue in games with even numbers of matches each round (aka 1v1, 2v2, 4v4 etc). Odd numbers of matches allow one team to try fighting back
(7) Fleets are often able to fully repair all of their damaged ships/squadrons after a game: 2 - winning fleets repair very quickly, losing fleets struggle to make repairs
(8) Spynets, Repair Yards, and Skilled Spacers are roughly of equal value: 1 - repair yards are overwhelmingly the most important resources to capture.
(9) The three Base Defense objectives (Fighter Wing, Planetary Ion Cannon, and Armed Station) are roughly of equal power: 3 - all 3 are good, but Fighter Wing allows players to deploy up to 5 additional squadrons at no cost which can have an important effect.
(10) The nature of the campaign favors big, hard-to-kill ships over smaller but more fragile ships: 3 - at the start of the campaign large ships are a potential liability, but at the end they are a critical resource.

I am not reading the other answers so as to not be influenced. I do not have very strong opinions on these particular questions, nor do these questions seem to capture the aspects of the Corellian Conflict that really concern me. (They concern me about as much as asteroids do.)

The exception is the grow-too-quickly question. I would prefer for fleets to grow more slowly. I also really like @ricefrisbeetreats's idea of not allowing any uniques at the beginning, and using veteran tokens to purchase uniques.

(1) The Difficulty-to-Reward for the Rebel and Imperial special objectives (Hyperlane Raid & Show of Force) is even between the two factions' objectives: DK
(2) The "Show of Force" Imperial special objective is too hard for the Imperials: 1 (does not mean I think it is 'too easy')
(3) The "Hyperlane Raid" Rebel special objective is too hard for the Rebels: DK
(4) Fleets expand and grow too quickly in the Campaign: 4
(5) Limiting starting fleets to one-upgrade per ship is a good idea: 4
(6) When one side gains the momentum in the Campaign, it is too hard for the other side to swing it back: 2
(7) Fleets are often able to fully repair all of their damaged ships/squadrons after a game: 4
(8) Spynets, Repair Yards, and Skilled Spacers are roughly of equal value: 1
(9) The three Base Defense objectives (Fighter Wing, Planetary Ion Cannon, and Armed Station) are roughly of equal power: 4
(10) The nature of the campaign favors big, hard-to-kill ships over smaller but more fragile ships: 2