When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
Very possible the tires are "out-of-round" due to sitting in one place too long. It can create a flat spot or bulge the tire. Result: wobbly or bouncy ride. Shocks could be stiff also due to lack of usage.
I think you will find the old bias tires are just out of round. It is possible (they tell me, never my luck) that they will round out after you drive them some. If all 4 are out of round of have flat spots she will really dance. Radials are the answer.
I had an old motor home with Bias Ply tires and they always started out ruff until they warmed up!! it used to worry me till I got used to the pattern and started just waiting out the bouncey ride.
ANother thought is that the trucks originally rode like h_ll unless the had a load on them. Remember these were actual trucks designed for hauling and for farm use. Springs were strong enough to put some hay in the bed and deliver to the field.
I went over a local RR track that was not thhest and my frined following me said the truck came off the road about a foot and a half.
At the very least I'd try radial tires, just for the improved ride and handling.