Just as a test; try putting 4- 50 pound bags of sand in the bed against the tailgate and test drive. That may stop the rear bounce. Also, was the steering box rebuilt or just adjusted the 50+ year old gears? Might still be play in the box. There is a steering stabilizer made for these trucks. It will dampen the front end jerking. streetperformance.com look for MOOG steering stabilizer SSD42. Might help.
