360 motor in 1972 Dodge Demon vibrating

If there was a mechanical imbalance it would be felt all the time the engine is running, and if revved in nuetral or park it gets worse. around 4K you'd be panicing, not losing screws. I would suggest some basic engine diagnostics in addition to looking at the flexplate, convertor, and harmonic balancer. A simple compression test will show a bad valve or weak cylinder that could be causing a milder shake that smoothes out at times.