Even requiring two advantages, auto-fire is pretty bananas in terms of raw damage output vs a single target. I think a simple fix is to only allow it to be used to hit multiple targets, so no stacking multiple hits on one target. So an autofire weapon is really good at taking down or damaging multiple targets, but not particular good for focused fire. That makes higher damage non-autofire weapons more attractive if you're just trying to take one person down or harm high soak individuals.
Agreed with most posters, the X-Wing shouldn't be so obviously better than all other starships that you'd never want to fly anything else. I think going down to armor 3 or 4 would accomplish this pretty well.
Also, I'm fine with the X-Wing being the default choice that is a little more powerful than most ships, but I shouldn't feel like an idiot for wanting to fly something else.
Oh, good idea about upgrading the check instead of increasing the difficulty. At the very least, I think that makes a lot of sense after difficulty 5 (normal max difficulty). Some of the mods, such as the hanger bay, go up to 5 mods of the same type, which would mean 7 difficulty dice for the final mod!
A couple thoughts:
-Shields: These add black dice to defense rolls, not soak. So they make it harder for enemies to land a hit in the first place. A TIE attacking a YT-1300 with standard shield configuration would have a difficulty of two purple dice and one black die to hit, and of it scores a hit it would be doing it's damage against a soak of 3, so if it scores at least one success it will do 4+ damage (6 base damage + 1 or more successes - 3 soak).
-Minion Groups: In my opinion, minion groups are basically good for two things - streamlining fights and making PCs appear more badass. In most cases, grouping 3-4 TIEs together as one minion group makes them easier to fight than if they were all fighting separately. That's because, even though they have a higher chance to hit, they are taking a lot fewer shots, which probably means less damage overall. Similarly, they have one pool of HP, which means the PCs only have to break through their soak once and then can potentially take out multiple TIEs. Typically, when I am preparing a space battle, I want the PCs to be fighting 2-3 ships or minin groups, so I'll group the TIEs or whatever craft they are fighting into groups accordingly. So if I want a relatively straight forward fight against 4 TIEs, I might have two groups of two.
-Strain: Unless enemies are doing ion damage and specifically trying to disable the ship (ion damage does staring damage), it's typically only going to take strain when the PCs take extra maneuvers in combat (two strain to take an extra maneuver) or things like push the limit. You may also consider applying staring if they roll disadvantages on pilot checks or in any other check where you could see some misstep causing stress to the ship.
I'd be surprised if 4 encounters took less than 4 hours, especially if one or more of them involve a fight, especially when you consider all the banter, preparation, and side encounters the players are likely to initiate.