360 Engine issues

I'm assuming your oil pressure readings are at a normal idle? If so, good. If not (say 1500 RPM hot, then you need to pull the engine and pull the pan and see what's going on with bearings). Unless the engine has been modified, a 360 should have weights on the converter, or, the special aftermarket flex plate made for an externally balanced 360. If the balancer has any wobble, or, the rubber is deteriorating and coming out, it needs to be replaced. Pulling the pan with the engine in the car is a real pain. If you're going to replace the flex plate or converter, do it while the transmission is out. If you have to do more to the engine, I'd just pull the engine out and make it easy on myself.