OK...just to add more grist for the mill...do you have access to a Holley carb, say, a 600 or the proverbial 3310 750? (Now all you guys just hang on to the "But you're a Carter guy" comments for a sec...) He's changed everything except the carb and the cam. Holley's out-of-the-box seem to tolerate big cams better than Carter/Edelbrock's, so my thoughts would be to try a different brand carb and see what shakes out. Could be that 1406 just doesn't like Thumper cams.....
Just my $0.02