FWIW, I took a chance on one of these CMI cards. ($10 shipped, figured I could stand to lose that.) And, I dunno, maybe it's just my board or I'm using the wrong driver set but so far as I can tell these cards are nearly worthless. It works perfectly with Commander Keen (that seems to be a "thing" I'm picking up while playing with various alternatives, everything works with Commander Keen) but nearly everything else is broken.
Jazz Jackrabbit: No sound or music
DOOM: Crashes on startup
Quake: Repeats the same fragment of digitized noise over and over again
Apparently the card relies on having the PCI IRQ initialized to something that's useful for DOS; initially my board insisted on assigning it IRQ 10. I screwed around with the PnP settings until I managed to convince it to get assigned to IRQ 5, but it didn't fix anything. Given Adlib seems to work (the aforementioned Commander Keen) I'll guess it's an issue with ISA DMA.
A bit disappointing since it looked like that VIA chipsets were usually on the more compatible side for this sort of thing, but live and learn.