If the OP's main concern is rushing, maybe he should just increase the mission time limits?

When you've got only like six rounds to hit four objectives that take multiple rounds to get to, it doesn't make a lot of sense to stop and fight unless you absolutely have to.

I have to say, I don't really care for the time limits, or the required rushing, either. Mostly they seem arbitrary and "game-y". I feel like the threat system should be facilitating the sense of time pressure on the Rebels.

"Hurry! We need to reach the control center before every Stormtrooper in this sector gets here !"

vs.

"Hurry! We need to reach the control center before we miss the 3:19 Uptown Express ! We don't have credits in the budget to get a taxi!"

- H8

Its not the uptown express you need to worry about missing, its the 20 some odd little balls of death blowing up the express you need to worry about. You are racing against the reinforcements, you just dont fight them due to their massive amounts of death bringing ability.

That gives me an idea. What if, instead of ending the mission when the round limit hits, you just deploy the rest of your imperial troops? Not just the ones that are in your deployment hand, but everything you have. Vader, Wiess, IG-88, Trandos, etc. Everything that's not already deployed gets put on the board, wherever the Imperial player wants. No limits, no holds barred. And the Imperial player gets to deploy anything that gets removed from the board the next round. This goes on until the mission objectives are completed or all the heroes are wounded. This probably won't work universally, but at least for the missions that have text that reads something along the lines of "There's too many Imperial forces overwhelming you..."

Unfortunately would not work. We have often found that on the timed missions the Rebel players loose by 1 activation, or even 1 action. Just having more bad guys on the board would not be sufficient to not allow the rebels to just win on the next turn.

Ok, it isn't always that way, but those cases where extra figures on the board would be an impediment the likelihood is it wouldn't make a difference anyway as usually in those cases the Rebels are poorly placed or so badly boned what is already there will be sufficient to prevent their victory.

Unfortunately would not work. We have often found that on the timed missions the Rebel players loose by 1 activation, or even 1 action. Just having more bad guys on the board would not be sufficient to not allow the rebels to just win on the next turn.

Ok, it isn't always that way, but those cases where extra figures on the board would be an impediment the likelihood is it wouldn't make a difference anyway as usually in those cases the Rebels are poorly placed or so badly boned what is already there will be sufficient to prevent their victory.

I'm envisioning a situation where the rebels are one activation away from completing their objectives, let's say, escaping to the entrance. Then, when the mission "ends", here come the reinforcements. Drop an AT-ST, Elite Royal Guards, and Probe Droids on/around the exit, blocking it off. If the Rebels can still punch through, victory. But most likely it ends in defeat.

You could add some sort of risk/reward feature that allows the rebels to "escape" when the allotted mission time is over, or they can keep playing with increased Imperial reinforcements pouring in. If they continue, and still lose, then the Imperial would get an extra influence or XP. If the Rebels win, then they would get the bonus they would normally achieve. That also adds some kind of penalty for withdrawing, trying to stay on topic.