You might want to inspect your rear shoes to see if they're contaminated with gear oil or brake fluid. I drove a 64 for years without ever locking up the rears.
Good luck,
Scott

Scott Ward

2 1948 1.5-ton Loadmasters
The red one and The snow pusher
1 1950 3100
1 1955.1 Chevy 6500
1 1954 Chevy 6500 2-Ton
1 1955 1st Series COE 5700
1 1963 K20 (454)
1 1964 C10 (350)
1 1951 1.5-ton Dump Truck
1953 and a 1956 Ford F800

Raising a teenager is like trying to nail Jello to a tree!