You could try using the latest Snes9x intermediate revision (from
here, revision 92 or newer). That version should have no desyncs in this game (or any other game for that matter). As for the weird sound, well I haven't looked into that but maybe if you actually use Snes9x 1.51 instead of 1.43 (so, from
here instead, revision 60 or newer which should also have no desyncs), and also make sure Sync Sound with CPU is checked, it might sound better.
Do make sure "volume envelope reading" is off and "fake mute fix" is on, though. Those might actually be a part of the reason why the sound is so weird, but currently I think they can still cause desyncs in some games if you don't set them that way. Also, if a movie you've been working on desyncs reliably now with everything set up like this on the newest version, then unfortunately that probably means your movie has a desync recorded into it, which is better fixed by starting over than by fiddling with options.
(By the way, I'm not just suggesting these versions because I think it might fix the desync problem. I'm fairly certain that they do fix it. I found a bunch of desync problems in the savestate and initialization code recently and addressed them all and verified that in this game in particular (and several other games), even if I save and load a savestate every single frame, it doesn't desync, even if I count "one byte somewhere in the emulation state changed invisibly" as a desync.)