Might be worth 10 minutes to check the leaf springs and all hardware - brackets, shackles, hangers, u-bolts, etc.

I had weird clunks going between P-D-N-R, and handling issues. Discovered both sides rear end of the leafs were not attached to the frame, just sitting there by gravity, the shackles were rusted away. Fixed and clunks went away.

Would not explain your transmission issues though.