After wasting an incredible amount of time, I finally discovered the underlying issue: this board doesn't support Thunderbird core CPUs which is what the 800 is. With all of my troubleshooting I sometimes wondered "Maybe this CPU has issues?" and wished that I had a second Slot A CPU I could try, but I was sure this was the only one I had. Then I discovered that I had another, a 650 MHz Pluto and once I installed it, all issues disappeared!
The Thunderbird will work with the original BIOS, though it will occasionally have a glitch. But with just the right settings, it will work correctly for many hours, completing Memtest86 and every benchmark you can throw at it. But if you should try a later BIOS with that CPU, it isn't at all happy. At some point I forgot that I had both of these, and grabbed the CPU that I thought I had gotten with this motherboard.
TL:DR the motherboard is fine with the most up to date BIOS as long as you are using a CPU the board actually supports!
A lot of times when you first start out on a project you think, This is never going to be finished. But then it is, and you think, Wow, it wasn't even worth it. - Jack Handey