Sometimes an excessive amount of wheel weight can be corrected by spinning the tire a 180 degrees around the wheel and then rebalancing. Might try another shop to do the balancing.
On my 67 I am running 29x12.50x15 Sportsman Pros, They fit fine, but to answer sydcuda's question, Yes, I have a 1" plate mounted between the front spring hanger and the frame, works good!
I'm running the MT Sportsman Pro's they work well. The wrinkle wall construction really helps with a lower pressure, and the tread compound gets quite sticky if you burn em before you launch em. Note you do need to install tubes in them.
Just my opinion!