I don't want to want to put all my eggs in one basket, but I think I may have fixed it...
I swapped 2 of the cards around (Only two, because the rest needed to stay in their places due to size and possibly hard-coded restraints):
nVidia GEForce FX 5500 (Stayed because AGP card)
ExpertColor S3 Virge (Stayed because it's part of the AGP/PCI video card swap feature)
Hauppauge WinTV (44371) Card
Sound Blaster Audigy 2 ZS
VFX1 VIP Decoder Card (Cable-attached to ExpertColor Card) (Stayed because ISA, and too big for bottom slot)
SB16 CT1740 (Stayed because ISA, and too big for bottom slot)
Etherlink 3C509B-TP ISA PNP Ethernet Card (Stayed because of size constraints on motherboard)
I turned off the IRQ for the USB ports (I don't know why they're needed), which is what I've read other people doing when they have problems with resource conflicts.
and finally, I installed the P2B chipset software utility: https://www.asus.com/Motherboards/P2B_MB/HelpDesk_Download/ (I didn't want to do this, because the last time I tried, with my previous motherboard, it seemed to install a copy of each already-existing device file, and actually severely bogged down the system so much that I had to reinstall from scratch.)
It seems to have added some logical devices that weren't there before, and everything seems stable now. Doom II has no choppy sound, doesn't crash randomly, and Duke Nukem 3D starts up just fine. I haven't exactly tested Jazz, but I could probably assume that it works just as well.