A bottom line to consider is most GB emulators do not emulate a SNES. That's required for the full suite of Super Gameboy enhancements.
You'll have to check if the music in question uses the SNES sound chip in any way.
I did check in bsnes, and it sounds perfectly well running in super gameboy mode, but I think this is just down to maybe better emulation? the only SGB audio enhancements I can find listed for it are changes to the credits theme and a sound clip for Pauline's "HELP!", I'm gonna check some other GB emulators and see how they stack up vs SGB mode.
Okay, back with initial tests, comparing performance with DK GB and Rolans Curse 2.
Higan, default setttings, very bad sound all around.
VBA Generally bad sound with DK, lag spikes in RC2 that had sound dysyncing and then struggling to catch up.
bsnes/SGB, Good sound in DK with occasional lag spikes, Same with RC2.
Result: DK GB is slightly more cpu intensive than standard GB games,
Higan is slightly more cpu intensive than standard emulators,
VBA kinda sucks,
bsnes/SGB is oddly stable,
And my laptop is shitting the bed again, as evidenced by the fact I just had half my screen go missingno
