I'd yank that silly IBM ATOnce clone thing but quick. Probably the point of contention in the system too. Yes, yank the 68000 off of that and reinstall directly into the CPU socket. Be careful to observe correct notch orientation.
Why "silly" AtOnce?
What's so silly about it?
Back in the early ninetees I was really glad to have a Vortex AtOnce286 classic in my A500 because it allowed me to run all the MS-Dos soft we used at the CAD school (dbase, word, fortran, c and qb).
(For CAD itself I had DynaCadd plus a tool to convert the 3d CAD data to CNC files for the CNC milling machine and CNC lathe - was slooooowwly, but worked)
Best way to clean IC pins is to simply remove and re-insert them. The friction of the sockets is usually enough to "clean" 'em. If they're truly oxidized, get yourself some very light grit sandpaper or a fiberglass brush to clean 'em up.
Why not an angle grinder? (just kidding)
I always use commercial contact sprays for contact problems, as they're non-destructive in contrary to sandpaper and the like.
I'd be willing to be though most all of your problems will be solved once you get that AtOnce board out.
Really not sure why you thing the AtOnce causes all the problems...
All the chips, but especially the Kickstart, CPU and Agnus chips all deserve to be re-seated.
Fully agreed - but do not forget to treat them with contact spray...