I have been running radial tires on all of my cars for the last 30 years with the stock wheels and have had no problems. And I don't baby my cars either.
When I restored my '55 Special I used a Dyna Flow from a '55 Super which had been rebuilt. I used the tail shaft and housing off of the '55 Special Dyna Flow and it all worked out great.
My house has a large two car garage and I have a 30' x 50' steel building where I have my shop and store 4 cars there. I have another 12' x 20' steel building where I keep my Jeep and spare Buick parts.