Check that the brake shoes are in the correct locations.
Grabbing/bouncing from the rear brakes is often because the leading and lagging shoes are reversed on one or both wheels. It's even possible that two leading shoes are mounted on one side and the two lagging shoes are on the other. This condition is listed as the #1 cause of brake grab in the GM service manual (see below).
It is possible for this condition to develop because the brake shoes are identical (and can be mounted in any of the front/back or left/right positions). However the are lining material that is bonded to the shoes comes in two different lengths that are specific to front and back.
The difference is subtle and not so easy to see - especially when the liners are on the shoes. Both liners start at the same spot on the bottom of the shoe, but the front liner ends about 1/2" lower than the rear liner.
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Here is a complete NOS rear brake assembly that has been in storage for 30 years and was never disassembled.
Bottom view:
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Top view:
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From the GM service manual section on Troubleshooting Drum brakes/Rear/Grabbing:
REAR DRUM BRAKES
Causes
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1. Shoes/Linings incorrectly installed. Each side should have a leading and trailing shoe. The lining surface on the trailing shoe will be slightly larger than the lining surface on the leading shoe. The trailing shoes should be installed in the rear position on each side, while the leading shoes are installed in the front position on each side. If the shoe positions are reversed, the braking performance will be very grabby and prone to wheel lockup.
2. Brake linings contaminated with brake fluid or gear oil.
3. Incorrect shoe size or type.
4. Loose or broken brake lining.
5. Brake shoe adjustment too tight or too loose.
6. Weak or broken return springs.
What to Check For:
Look for the following common mistakes:
Leading and trailing shoes are reversed.
Both leading shoes are installed on one side while both trailing shoes are installed on the other side.