I played a bit with the IIgs emulation and found that GNU/Linux Mandriva 32bit running SheepShaver seems to work best.
All sounds seem to play reasonable and Bernie freezes only occasionally.
I happened to find a copy of DPaint_II, which I had with my Amiga. I never expected to see DPaint again, actually.
Does anybody know what file types are saved by DPII with the Apple_II?
Obviously there is also the Mac OS X version of Sweet16, developed by Eric Shepherd, based on Bernie ][ The Rescue.
Sweet16 can mount HFS formatted DMG images for swapping files.