I figured it out. Here's what I came up with incase anyone else wants to do this:

You need these files in A:\ULTRASND:

1ULTRAMIX.EXE (24018 bytes)
2ULTRAMIX.INI (769 bytes)
3ULTRASND.INI (5476 bytes)
4ULTRINIT.EXE (29680 bytes)
5              ~60 kB total

And the following lines in AUTOEXEC.BAT:

1SET ULTRASND=240,6,7,11,11     (or whatever your card is using)
2SET ULTRA16=34C,0,0,1,0        ( " " )
3SET ULTRADIR=A:\ULTRASND
4A:\ULTRASND\ULTRINIT.EXE -dj

Note on SET ULTRADIR: ULTRINIT updates ULTRAMIX.INI so it needs access to where that file is stored. If once the system is booted you want to put in removable media (CD, ZIP, etc.) with the full ultrasound installation (pats, etc.), you can update the variable with another SET ULTRADIR command but the current ULTRAMIX.INI will still be on the floppy so you might need to copy it over.