Using the left trigger as a modify key I should be able to get every command of any note on the controller, even including all the communications options to tell other ships to form on your wing or head home etc. I played around with it a bit last night and I am going to finalize my joystick controls tonight. I was also afraid that the DRM in steam would make it harder to modify or use a different dosbox build, so I went with GoG for those reasons. Out of the box Dosbox only allows for a 4 axis joystick and the 360 controller has 5 so there's some issues with the right analogue stick, but there's a different dosbox build you can get that increases that limit to 8 that I got working with x-wing last night. Dosbox will recognize a 360 controller and you can use the internal mapper (Control + F1) to add controller events for all the key presses you want.
I think Steam only had the original disk version and the windows 95 CD version. Steam might include that version but I could not tell for sure. The GoG version includes the '94 CD Rom version which I think is the best because the newer CD version uses actual CD music, which may sound nice, but is not at all plot specific.