If the GN stock trailer pulls fine behind this same pickup, then you've got tire problems on the flatbed. 

Possibly jack up one side (then the other) and spin the tires to see if one is horribly out of balance.  If you don't find it that way, probably a tire with broken chords.  Should be able to see that by looking at the tire when spinning it (while checking for balance issues).  If theres a chord broke, it'll have a bump (possbily pretty good size), but won't necessarily be out of balance. 

Chords can break when sliding tires sideways as in turning very short, btdt.