You should check your size carefully. That doesn't sound like an F150 size tire. In 2010 the Platinum would have come with 275/55R20, not 65 series. Furthermore, terra grappler G2's aren't even available for 20" rims according to their own website, so the fact that you can't find them on Amazon, well, might be true everywhere for that size.
I don't see a problem running a slightly different tire on a pickup front to rear in terms of tread pattern and wear level as long as they are the same size... Most modern vehicles with AWD and 4x4 systems operate in either an "open center" diff or "2wd with modulated clutch to the other axle" mode for normal driving, both of which allow for plenty of "slip/differentiation" between axles for slight differences in tire size.
The Hankook Dynapro AT2 and Westlake SL369 would be options on Amazon that are similar to the Nitto tires in terms of tread pattern to keep things "looking right."
Personally, I would not usually buy tires from Amazon. Tire's are one of the only things I do not work on myself. It's not worth it. Tire shop time is super cost efficient and cheap compared to how long it would take me to fight with home-jobber equipment to mount tires with. I'd much rather buy the tires and installation and TPMS and road hazard certs direct from the shop that will be installing them. This "packages" the liability for the tires into a neat easy to define circle. Use the Amazon card some other way.