The HEI does use a smaller diameter dist shaft. The stock dist has a larger dia shaft that fits tighter in oil pump drive passage. So any deflection will show up as a wobble, as the HEI shaft is supported by its shaft bushings and the top of the oil pump.
You say that like it doesn't mean anything. THIS IS THE PROBLEM. Or at least what started the problem. The gears have been pushing away from each other to the extent, the gear teeth are only making partial contact. As for replacing the cam. You'll have to make the call or get really good pictures of the cam gear.
I've seen one of the 6cyl HEI with the smaller shaft. The shaft is the same size from the top to the bottom of the gear. The bottom is turned smaller to fit a different bushing. On a 250 the bushing is in the block, not the pump. Are you sure the guy that sold you the dist knew what engine it was for? The dist I saw was in Pontiac Ventura (Looks like a Nova) with a 250.
