I know my truck gets a lot flex so I hope mine holds out. I can't put a roll and lock type cover on it because it opens up when I drive around. Mainly would do it on the turns where I am off side to side as well as on a grade. Hard to explain... My extang cover stays on, but when it gets frozen to the point the tailgate won't open, I just drive it around the block you can hear the ice pop out from underneath it as the truck bed flexes.

 

They do flex a lot, but mostly in the sections aft of the cab. One ought to be able to measure the misalignment of the radiator mounts if you back the rear end askew up a ramp. I haven't looked closely at the mountings, but if it is mounted on 4 corners then removing one of them should also solve the problem, as long as the radiator didn't fall out.