I recently had to make a tire decision also.
The F range Toyo tires are the 35X12.50R18LT which have a capacity of 3970 lbs.
Those are somewhat oversized and pretty tall tires.
They don't seem to have any more capacity than the LT285/75R18 which are 4080 lbs.
If you go down in sidewall ratio, at a LT285/65R18, it's still rated at 3640lbs E rating.
I have the Nitto Terra Grappler G2s on my truck, in LT285/65R18 size, which have less sidewall flex.
The LT285/75R18 Nitto's are Toyos performance line, and are rated at 4080 lbs. However, I didn't like the sidewall height.
You get noticeably less sway with a 65% sidewall height ratio.
2016 F250 CCSB 4x4 6.2L
2001 Lance 820