After some more improvements, Windows 9x seems to run fine with it.
So does DOOM (and DOOM II). Although those ran before already.

Running test-sbp.exe somehow makes it run into a ARPL instruction that keeps faulting to itself when selecting the DSP audio test?
It could be HIMEM.SYS though.
Edit: Nope. Without HIMEM.SYS it still happens.
It's actually executing an ARPL instruction somehow.
Edit: It literally crashes on that instruction after sending a DSP Enable Speaker command. Either that or the executable is somehow corrupted during the installation process.