Thank You Frank, for getting back with this valuable information. A few things come to mind.
Did you replace your rear springs? This would set a new height to the rear of your Squarebird.
In my opinion, the reason you could not push the rear down with urethane in the clappers is because there was restriction of motion caused by the clappers. This caused the rear axle assembly to roll which transfers torque to the upper arms. That is bad because it caused so many upper arms to tear out of the frame. Rear end motion should be straight up and down in a linear motion. The parallelogram arms should have freedom to accomplish this throughout the full range.
Full extension of the axle should be limited by your shock absorber stroke, not clappers. I see NO good reason for the clappers whatsoever. Instead, I do see how they are a direct cause for damage to rear end parts. Honestly, if I had a '58 Squarebird, I would cut the back half of the clappers off so that the axle regains full freedom of motion.
The clappers do not offer any strength to the assembly and they should not determine the ride of your Squarebird. The ride is determined by your shock absorbers and springs. Clappers restrict motion by binding. Does that make sense to you? It sure does NOT to me. - Dave