from past experience on a s/c mini i knew, coud it be that the bearings are strving of oil as the boost is pressuirsing the sump by blowing past the rings, and the cugging is due to the oil starvation and cavitation.
long shot but possible.
also the s/c should be making consistant boost not risiing if a toyota ageze model, is it starving uder low revs and the secondries opening up making it run ok later on in the carb? might need larger idle jets depending on carb.
also sounds like dizzy or vacume advance.
with boosted angines i have always been told to lock the dizzy timming to prevent problems. lower hp overall but no tuning problems