I agree, the 285/75/17 would be a good option if you are concerned as to fit as it is only .6" shorter, but over an inch skinnier.
Tire size converter online has them as below:
315/70/17 as 34.4"/12.4"/17
285/75/17 as 33.8"/11.2"/17
I'm running 35x12.5x20 on my F250 with a leveling kit. I did have a slight rub issue on tight turns on the driver side but the dealer was able to tweak it and its good now. Not sure on a F150.
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