I'll give you some info, but you'll need more I'm sure.

First, find a new way of meeting and evaluating "mechanics". Anyone who would suggest a trans change or a rear gear change to correct an engine operating problem is clueless.

Second, by your own description you usually operated in the 0 - 2500 range, but the Lunati cam you listed is intended for 2000 - 5500. I'd say you are definitely over cammed, which is probably contributing to a vacuum problem, which will affect your advance. Those things may be what's contributing to pinging, I doubt you're having preignition. The run on is probably caused because the idle linkage screw is in too far leaving the butterflys slightly open at shut down. Cam specs would be helpful, e.g. duration, overlap, etc.

Third, if you're getting rich fuel condition out the tail pipe your cats are wasted. Since it sounds like you've been wrassling with this for some time, they've probably been overwhelmed with HC and are spent. Could be your carb is set up wrong, but with the other issues you need to approach this one problem at a time and avoid the "change everything" approach. (similar to the trans and gear thing).