Update:
While I could get the system to accept the audio drivers without any problems for both DOS and Win3.x, the big issue was that I couldn't get my Mitsumi-Quad CD-ROM working with it (I have to go through the soundcard since the mainboard doesn't have an IDE slot for it) -- Even when using the generic IDE connection slot on the card.
I could make guesses as to why it wasn't working, but even when I merged the CD-ROM drivers from VOGONs driver wiki (Which includes the OAKCDROM.SYS file and setup) with the linked drivers for card off Internet Archives, it still seemed to not work too well.
I've switched back to my Sound Blaster 16 which decided to stop having the I/O conflict it was having earlier after an OS re-install. Still have to run the Diagnose program to get it to initialize the SB16's CD-ROM recognition, but only once during any given session, and then it's happy to accept CD drive.
I'm kind of sad about this because it seems like a neat card, and since it's not one of those later Sound Blasters with the DSP problems which suffer from Hanging Note Syndrome, it seemed like a good alternative, despite being something of an unbranded piece of hardware. Still, if anyone comes up with a solution for this particular card using a mix of drivers that plays nice with CD drives that -MUST- go through the card, I'm happy to hear about it!
Cheers!