I've spent some time and ironed out any other issues, but I'm having a consistent issue with targeting. Namely, whenever I select next target, it seems to select closest enemy (I'm guessing, because it selects an enemy every time). I have a Thrustmaster T16000M mapped to use the keyboard commands, and have confirmed it's sending the inputs correctly, only the one keyboard input. I'm a bit perplexed by this, is there any suggestions I can do to help with this?

It's possible the software doesn't override the default game setting for buttons 3 and 4.
If you are using any of the DOS version the game supports up to four hardcoded buttons that can't be changed and one of those is the command for targeting the nearest fighter (the other is the button to make the cockpit disappear).
With my software I usually disable the directx function for every button but 1 and 2 and the others are set to only give keyboard commands without being picked up directly by the game (which basically reads a 2 button 2 axis joystick plus keyboard).
Just check in your software if you can do the same.
I have a CH Products HOTAS and its software was originally made by Bob Church, the same guy that developed T.A.R.G.E.T. for Thrustmaster so it probably has similar functions.

Unfortunately, the button is on my throttle, which isn't even recognized by the game, so it can't be that. I've also noticed that the time compression button on the keyboard just ejects me, so I'm a bit perplexed.

I've done some more testing, and it appears this only happens on the very first mission so it may be just a bug that I don't have to deal with anymore. Strange.

Edit: Actually, it seems to consistently only happen with the shuttles. Anytime there's one of those nearby, next target always targets them.