balanced flex plate on balanced 360 cid

That is a problem if you don't know how to contact the builder but like Brian said if the balancer was on it when you got it it's probably right and the flexplate is most likely the culprit. It makes sense that they'd internally balance it for the RPM they were spinning it. Not that you can't spin an externally balanced engine that high, they just live longer when internally balanced so most shops that build an engine for real high RPM internally balance them. With that said I bet the problem is the flexplate. You probably just need a neutral balanced flexplate like a steel crank 340 or 318 would use.

p.s. what torque converter are you using? Does it have a weight(s) welded to the front (engine) side? Like it was mentioned earlier it can also figure into the equation.
I believe you are right and plan to split and install neutral plate. Torque converter came with car 904 . Only thing done to transmission was rebuild kit so it would be a stock converter I believe. This vibration is with car in park. The vibration changes speed with morer RMPs.(vibrates faster) Sorry about spelling and gramer .I need to figure out spell check . And thanks for you help How old are you?