I put load range E tires on my previous F150 (pre tpms). The ride was a little harsh, but I adjusted tire pressure for the load. In hindsight I should have stayed with D's.
My current F250 has load range E's also, and rides real harsh. Ford's tpms requires 65 psi front and rear, but I can get away with 60-62 psi without setting the stupid alarm off. It's been years since I researched everything, but I believe I could run 40-45psi unloaded if not for the tpms alarm.
The tire programmers and procedures for my truck only allow for swapping front to rear when the fronts are at a lower psi (OEM specified) when rotating tire positions. The only solution to run my tires at 45psi I found was to put the sensors in a pressurized PVC pipe and let it roll around in the bed (YouTube). I have no idea if it actually works.