I had the same problem with a set of bias plys on my T-Bucket. Tires about the same size on 12" wide Weld draglite wheels. One day would be smooth, next day they were horrible at anything above 45 mph. They would smooth out somewhat after about 15 minutes - those flat spots mentioned earlier. Had them balanced half a dozen times, using static and dynamic techniques - all no good after a couple days. When they were not smooth, you'd swear they felt like you were riding in an old Huey.
I then tried a set of 16.5" wide Hoosier pro-Street radials. Definitely better, but still not good at highway speeds.
Then went to a narrower radial with a lesser sidewall load rating on an 8" wide draglite. Now that fixed it all. It appears that the car just wasn't heavy enough on the rear axle to 'make' the tire roll smoothly on the large tires. I believe the centrifugal force of the rotating tire caused it to eventually get slightly out of round (perhaps after hitting a bump) when you got it up to a certain speed - think of an old time pizza maker slinging around the pizza dough over his head. The stiffer sidewalls of the larger tires didn't flex enough with the lightly loaded axle. You had to run about 5 lbs of pressure to get the flex on the larger tires but that was no good for general cruising especially at highway speeds.
Don't know how this helps the OP at all, but that was my experience with bias plys.