Im shure this geuss is way of base, but i belive that AGP 1x gives something like 700mb/s transfers. Im shure that wrong, but i know its a realy high number, and most lickly more than your current video card will need. unless its using ddr vram or something, witch im pretty shure its not. The only other thing that comes to mind is heat. You sound like a power user so you probably got fans up the wazoo, but if you dont, and you think theres any possibility of to much heat in your chasy, try takeing off the cover and putting a small desk fan somewhere around it to try and circulate the air. I know, realy off the wall, but heat could definatly cause this problem. Also, i know that ePSXe doesnt do this, but some games (like Diablo and a few others) leave behind an error log, usualy ending in .err or something, in the directory of the executable. you said youve crashed on Sims a few times, look in the executable directory for that game and see if you find any files with a recent date that you can read with a plain text editor, if you do and it looks like an error log, post it. If not then sorry, ill keep thinking, if i come up with anything ill post.
Good luck!