By that logic, you could splice in random shots from the saucer crash in Star Trek Generations. ;)

If you establish TOS bridge sound effects early on with the first Steve scene, you can carry that over into the crash and throw in the classic Red Alert sound when Stack says to sound the crash alarm.

I think you're on the right track with a little tightening up here and there. More Airplane lines could come over the cockpit radio. And Shatner could still be rambling on in the background after the crash.