I think the offset balance weights are on the center part an not on the outer ring. I could be wrong but if I'm right the outer ring just does the dampening and if it spun the only consequence will be the timing marks will not be right. I could definitely be wrong though.
I don't think it will run like that. not really sure what's going on with that motor but ifnit were mine I would try a different 50oz balancer and flywheel before tearing the engine apart to see what's wrong with it. It isn't a stroker bottom end is it? Could be mis-matched pistons/ rods / crank, etc.
Didn't get alot of info from the guy in N. Carolina when I bought it. He just stated that the motor and tranny had less than 5000 miles on them.
The block doesn't care what firing order it uses. The camshaft determines the firing order. Among the 302 roller cams, the HO, F4TE and the Cobra GT40 cam use the 351 firing order. The base roller cam uses the older F/O