I have a '54 3600 and have the original 15" split rims. I found a local tire shop that does truck tires and they put radials - uniroyal I think - on the rims and the run great. I noticed a hugh improvement in the handling, while keeping the original looks. My rims were in pretty good shape though and the guy at the garage said if they weren't he wouldn't have mounted them. He seemed most concerned with the lock rings and whether they were bent or not.
So my advice would be to find a Truck tire place and show them the rims before you give up on them.