Front Drum brake troubles on a 1964 Dart

When you drove it, did the steering wheel shake or the whole car.
Next drive, gently pull on the hand brake in the release position, so you can relax the emergency immediately, feel for shake.
If it shakes then, it indicates the rear brakes bent
Steering wheel shake, front brakes bent.
It's not unusual for new drums to need "truing" on a brake lathe.
The rears may need it also depending on those test results.
Take drums-hubs to an automotive machine shop, imho