Maybe it's an accumulation of various things? Is there play in the hitch head/shank/receiver? There could be play in the receiver. Maybe try strapping on a camcorder to see what is happening with the receiver. What tires on the TT and what psi?
What condition are the leaf spring and equalizer bushings in? Are the springs tired? I would check alignment on the TT. I would check the frame in the area of the springs hangers for cracks or damage. If the spring hangers are the 6" tall type and the axles are underslung, tying the bottom of the spring hangers together from one side of TT to the other may help control movement. Mor/ryde has a kit or make your own. Adding some good equalizers like Dexter EZ-Flex may help.
Quality shocks on the truck, such as Bilstein, may help. Adding shocks to the TT may help too. I've done both and they have helped a lot.
You have rebuilt the entire front end, but are you positive there is no play at all? I rebuilt the entire front end in our F250 with all high quality parts also and still have a little play. It could be joints in the steering column, I don't know yet and will have to get under when it's warmer out.
I have towed our 29' TT with our F250 with a Reese WDH and with and without the cam arms mounted. Without the cam arms, it's a real bear in windy situations and not all that great with "normal" sway. With the cam arms in place and adjusted, it runs great.
I've added a shim between the Reese shank and hitch head. There was what I thought was excessive play between the shank and receiver so I installed a Blue Ox immobilizer to remove the play. Have only done a short trip with it since, but it does seem to have helped.
