So, here is the statement in question:

"During each round, each squad must contain all ships and upgrade cards from the previous squad. Ships from the previous round must keep all equipped upgrade cards, and these cards may not be “transferred” to a different ship."

Does ship mean ship, like X-wing, or does it mean pilot/ship combo, like Wedge in an X-wing?!?

So, could I start round 1 with an Academy TIE, and round Two use Howlrunner in the "TIE Fighter" spot?

It means the same ship/pilot. Meaning you can only add to the previous squad, you cannot modify or remove anything (not even upgrades).

(At least that's how I've understood it anyway)

It means the same ship/pilot. Meaning you can only add to the previous squad, you cannot modify or remove anything (not even upgrades).

(At least that's how I've understood it anyway)

Exactly!

If you bring an Academy Pilot in round 1, he must be in every subsequent round. You can add Howlrunner in another Tie, but not switch Academy to Howlrunner.

After playing in an Escalation tournament a couple of weeks ago, I recommend keeping your additions simple so you don't confuse yourself.

The component list has "Ship Cards", and Page 8 has "Ship Card Anatomy".