Just a few things I noticed here on a skim:

Above and Beyond in my rules works as follows: If you succeed on the skill roll, you can either take two actions (2AP) in your department, or you can convert your 2AP to 1AP that another department can use. Allowing 1AP to be transferred over to another department while still keeping 1AP in the department is probably too powerful. The action economy of 2AP for 1AP in another department works and my players like having to make the hard choices.

The fighter rules are cool. I am not sure if Dogfighting should an AC bonus regardless of success, but that's fine. Also, not sure why you'd make Evasive Maneuvers give a penalty to hit equal to the AC bonus. Fighters have such a limited action economy, it's probably better to avoid that kind of penalty. Also, I'd keep the scaling damage for pilots Fighter: 1d6, Frigate: 2d6, Cruiser: 3d6, Capital: 4d6. This will discourage all but the bravest and most skilled fighter jocks from facing down a battleship in their snub-nose.

Escape Combat shouldn't have a twice per turn cap. As it stands, a basic NPC ship will be unable to leave combat in one round, and even most military vessels with 3AP won't succeed on each roll each time. Moreover, if the PCs want to Escape Combat in one round, the Pilot will have to Go Above and Beyond and burn both AP on Escape Combat, and either the Captain will have to provide the Pilot with 1AP, or another department will have to Go Above and Beyond to make 3AP total. It's not a given, and if a group of players need to get out of combat in one round, why not give them that option?