We are running bias ply tires, and the cars sit for a few weeks or more at a time. When I first start driving mine after it has sat for a while, I get a noticeable hop from what I imagine are flat spots on the tires. But after a few miles they round out and the hop goes away.
Also have your tires and wheels spun balanced on a really good tire machine. When they did mine they found one rim slightly bent (they are '46 Mercs, so who knows what happened to them in the past 60 years) and the tires are slightly out of round. Very characteristic of bias plies, they tell me. To show how critical it is to have perfectly round tires, a few years ago I bought the proverbial "Little Old Ladies Car", an '84 Ford Crown Vic with only 50,000 on the clock. She put brand new Michelin radials on it one time, drove it home, and never drove it again until I bought it 4 years later. Those tires still had the nubs on them, but from sitting they had developed flat spots, and even after driving the car for a couple of months the car still hopped like mad, the tires never did go back into shape. So I scrapped a perfectly good set of Michelins and had to put new tires on it because I was tired of the fillings in my teeth coming out when I drove it.
As for the front brake thing, yep, any rotating mass can be out of balance. On something like a 4,000 pound Buick front rotors that are out of balance might not be a problem, but on a 2,000 pound hot rod with a straight axle the imbalance would be VERY noticeable. One of the changes we made in my Son's T was to scrap the GM front brake setup and go to much lighter Wilwoods..........made a huge difference.
Don