I think I know what your talking about to a degree. My truck is the same SCLB which is the typical frame same as the CCSB. The vibration I was getting I figured was frame flexing or oscillation that I called frame bobble.
My remedy for it was to add crossmembers to my chassis.
I installed 2 additional cross-members directly above and below the transfer case output shaft. (3/8X6" flat w/1" solid square stock down length for upper)(3"channel lower)
Added another between the radius arm hangers. (3"channel iron)
Added a stiffener to the transmission crossmember which is also 3" channel because it fits inside track of the oem. Drilled three 3/4" holes down length to bolt them together. Also the two transmission mount bolts are used. I used 1" solid steel square stock from the transmission stiffener to radius arm crossmember and diagonally back 18" left and right frame rails.
This 100% stopped my frame bobble or bouncing. Truck drives and behaves much differently now. No longer leans into turns like it did and the biggest change is no more flexing like before. It feels like a shorter chassis to me for whatever reason but no more flexing bobble hop or whatever you want to call it.
One last thing you may try that's easy is: get a oil can and hit the leaf springs between leafs down the length. Make sure you hit all the Teflon slide points on the ends of the leafs too. This is no miracle cure but does help the leafs move back and forth on each other and is actually noticeable.
Good luck on it
That's kinda how my theory is on this too. Funny enough, I had it on my '87 F150 SCSB too and reading through the thread that sixOH posted, it spreads across many years (one guy had a '78 that did it). I've been working on a fix that is somewhat like yours and I'm glad to hear it worked. I just got all my materials and will be building a new x-member to bolt in.
My theory on this is with just how much material we have working/bouncing down the road and not necessarily the lack of strength our trucks have to hold it, but it doesn't support itself very well. Crawl under your truck and look, especially with us CCLB guys, there's a lot of blank real estate in between the trans crossmember and the back of the frame. There's a couple stamped crossmembers along the top of the frame, but they're more for body mounts, and IMO aren't doing a good enough job tying the frame together. So my running theory is that it's not a drivetrain vibration we're feeling, but a frame vibration. Both rails of the frame are moving at different rates (being pushed around by the springs/axle) because there's not enough crossmembers holding them together.
Now to answer the question "why doesn't it happen on every truck?" well maybe the trucks that it has happened to have done something in their "lives" , like going onto a ramp at a funny angle and getting a little frame twist, to work some things loose and that amplifies it bad enough for us to feel it. Also reading a lot into this I've found that some trucks haven't done it until 50k-100k into their runs. That makes sense, since now bushings are starting to wear and aren't holding the vibrations at bay as well as they once did.
We're not alone, google the "superduty hop" and you'll find tons of threads, articles, etc. I should have my new crossmember done in the next month or so, I'll keep you guys posted on the results
2005 King Ranch F-350: Studded and O-Ringed, BPD Oil Bypass, 205/30s, Stage 2 KC Turbo, ODAWG Ported Manifold, 4" TB Exhaust, Stage 2 AFE Intake, Billet Torque Converter, BPD 58V FICM, BPD Water Pump
2.5" Leveling Kit, 35s, Fusion Bumpers, ProTech Headache Rack, OnBoard Air, and a few other goodies