Hence the reason I suggested the balancer may be bad. Or maybe it spun on the shaft/sheared the :gay: stock pin. It is one of the few things common during all of those operating conditions. Downpipe or exhaust hittingthe body was mentioned I believe.
Next thing would be internals I think like a cracked crank, bolts coming loose from the flexplate (highly unlikely though) or converter bolts coming loose.
OR maybe crazy talk but,
Bent fan pulley shaft or fan hub? Just for the sake of finding nothing else, why not try removing your belt, start it and run through that rpm range and see if it goes away?
Sorry if idea's seem off the wall Mitch, but I have seen some really strange shit in my day and I find ANYTHING is possible!