I have an 08 450 that did the same thing at about 30,000 miles towing a 16,000# 5TH wheel. We were on a 7,000 mile trip when about half way through I was making a real slow stop for a red light, and at about 15 MPH it started bucking Very Violently. Felt like it would tear the 5th wheel hitch right out of the bed. Did the same thing again on a slow easy stop before we got home.
Took it to my dealer. He said I need to duplicate it with him along before he could diagnose the problem. They had no clue
I towed the same trailer 100,000 miles with a SRW F-350 with the same hitch with no bucking.
I found a Ford service center in a small town in Eastern WA, that suggested that maybe the hitch was not robust enough. It was a 20,000# Reese. After checking it out, there was some slop in it after 10 years and many miles, so I replaced it with a new 22,000# reese, and has not bucked again in 14,000 miles.
Hope this helps.