I'm very much leaning toward the possibility that I simply have a bad radeon card.
I killed Amidock (which for some weird reason, this time around Amidock didn't like that I was changing resolutions, normally it doesn't prevent it). This seems to have made it run for longer. But check this out! This time around I managed to extract AmIRC, while having IBrowse loaded, and started up EaglePlayer, loaded up the Xenon2 music mod, and had that playing. Then I went to check Aminet for some more mods and that's when I had the crash.
But listen to the awesomeness of Xenon2 during a crash!
I also am attaching the reason why I think my Radeon is bad... the heatsink appeared to be glued to the GPU... I had one that I had gotten from Elbox (64MB one) and took the heatsink off of it to see if it would fit better (the PCI1 on the Mediator wouldn't even fit with the original heat sink, the one I replaced it with barely fit in the slot, but I'm afraid it was still touching the busboard, so didn't dare turn on the system).
Well the 64mb had the usual two pegs holding the heatsink in, the 256mb one that I had in the system did not! Pried off the heat sink, and check out the nastiness!
My next thing is to swap it with one of the ones I have that has an active fan on it...
http://thefnords.org/amiga-crash.mp3.zipslaapliedje