After three more days of wrestling with this, I now have both systems working. On the Soyo K7VTA Pro, I couldn't get the USB 2.0 card and GPIB card working at the same time. Tried all the normal stuff of BIOS tweaks, moving cards into different slots, reinstalling drivers, etc without any joy. I thought, maybe this is "finicky VIA chipset" syndrome. So I concentrated on getting the (slower) Tyan S1830 going in dual boot. That was big fun too.
A few months ago I had bought a dead XP system for cheap off Craigslist, I wanted the XP Home product key, knowing I would need it for just this purpose. But when I installed XP Home on the Tyan using my install disk, it would not accept the product key! WTF?!?! It turns out M$ is very persnickety about XP versions, it won't accept an XP Home OEM key for an XP Home Retail install. So I used my present known-good key just to complete the install, and did an immediate "Home to Pro SP3" upgrade over it. (Yes, it can be done as long as the Home doesn't have SP3 installed.) I then used the same product key as the Soyo computer, which gives me 30 days to sort out which computer to use.
The Tyan is a very solid and stable motherboard, but its only a 900MHz P3. That takes a toll on update rate when using the USB scope. Maybe not a big deal, but I looked again at solving the problems on the Soyo. Yesterday I had the idea to start the whole process from scratch - remove the scope software, all USB and GPIB devices, uninstall their programs, delete all of their folders, go into Regedit and delete all entries having to do with them. There were multiple hardware keys in the registry for both cards.
I then installed the GPIB driver first (it is the older card) and then the USB 2.0, then the scope software. And voila, it worked.
So now I have 29 days to decide which system to use, and register the XP key with that computer. And I can happily boot to DOS, 98SE, or XP as needed.