I have new bias WWW on my roadster and 49 sedan (49 not on the road yet). The look is good but costly and ya struggle to keep it on the road at speed! And old tires sound scary! Your truck is probably similar to my roadster - not a good handling ride even on the best days. Radials would feel better, so it's the usual trade off. Then ya could go radial WWW? We drive our car a lot and I just don't like the bias feel - but man they look the part....
1 other observation, when the tire was on the spin balance, it wasn't spinning and rising up and down, as a circle would do when out of round, it was more of a wobble on the side wals, the tread patch seemed tru. Not sure if this makes sense, or not. Maybe the condition is not out of round but some other distortion. I mounted tires on the truck, switching backs to fronts, drove down gravel road 45 mph, and it hnadled not bad at all. But 45 mph on a rough surfac is not 55-60 mph on pavement.....
In my experience, the Firestone / Goodyear bias ply tires really give you a rough ride, follow the lines in the road, etc... The Coker Classics are almost as good as radials. They track and steer well, they are good in the rain and they give a pretty damned good ride. I have run them on a 59 Apache and now on my 50 Shoebox.
Just took this truck for a drive with bias ply WW tires still on. I switched front wheels to back and backs to fronts. 26-28 psi in tires, went for drive down gravel, to paved roads, then to highway. Had here up to 55-60 mph. Not issues with drifting or pulling and slotting. Vibration of course because tires are not balanced. Now I need to find a way to balance these sum bitchs, and perhaps, just maybe, I can use them. The tires corner not bad at all, braking is not quite as good as with radial tires on this truck. I do feel some rolling resistance, most likely the unbalanced tire condition. An old timer, told me to put on a few hundred miles, and see what I can do for balancing, don't know about that though. The tires felt good and warm afterwards, most likely the gravel rough surface of the last 4 miles......trust me if I wasn't frickin broke, would order both new tires and rims