Eh, If I was gonna replace FS music with VG midis, I'd probably try to find something a bit more appropriate then sonic. Though, I do have an orchestrated version of final zone from the first game that would probably be quite appropriate for some of the late game briefings. I'd tend to favor something with a more spacey origin though, maybe a few tunes from The Guardian Legend, maybe a couple from the Thunder force series.
But then, I'd also probably plug the battle theme from Magic of Schezerade in there somewhere, and Cervante's theme from Soul blade for the last couple of missions, so I may just be odd.
Here, try this one on for a briefing music for an important mission:
www.freewebs.com/phatose/thestageisset.midAs for 'converting' it, there are a couple of ways. If quality is a concern, you're best bet is probably getting a copy of synthfont and finding yourself a giant honking HQ soundfont bank, then using the play to disk feature. I believe the most recent versions of winamp can use diskwriter and the MS directmusic synth to create .wavs from midi files, though quality is only so so.