So in ten words or less 46 is the correct E Load Range number for the FJ?
The optimal pressure is dependent on multiple factors but the minimum should probably be to get adequate load rating and the maximum being the sidewall cold tire pressure limits. It is your own vehicle so do as you like but here is an explanation for the 46 PSI on the door sticker for new TT versions. It will take more than 10 words.
The 2013 FJ manual calls for tires to be rated at least 50% of the
gross axle load rating from the door sticker multiplied by 1.1 for P-Metric tires (
page 426). The P265/70R17 113S Dunlop tires do this and are rated for 2500 lbs at 32psi according to Dunlop. LT and flotation tires need more pressure than a P-metric to reach the same load rating for the same size tire. Due to the thicker and stiffer sidewall, the forces for flexing are higher and would generate more heat at the same pressure so more pressure is needed to reduce this and the tire might have a lower speed rating too.
How much pressure is needed to achieve the load also depends on the tire size since the rating is different at different sizes, not just load range or load index. The pressure has to be adjusted to match the rating of the original tire.
When putting P-metric tires on in place of LT tires for trucks and SUVs, then the load capacity of the P-metric tire must be reduced by a factor of 1.1. Although Dunlop says the GrandTrek AT20 tire is rated for 2500 lbs in P-metric, most charts have that size at 2535lbs@32psi so a LT tire must be at least rated for 2305 lbs (2305*1.1=2535) in the same application to maintain the capabilities of the vehicle.
"This load reduction factor is prescribed by Federal Motor Vehicle Safety Standards (FMVSS) and is based on the expectation
that passenger type tires (P-metric) may experience more severe loading and usage conditions when applied to light trucks."
The TT edition with LT265/75R16 tires, in single configuration can only carry 1910 lbs at 35PSI according to the TRA table. 45PSI is needed to get 2280lbs, 50PSI gives 2470lbs which could be load range C, D, or E. By interpolation, you can see that
46PSI is correct to replace the Dunlop 17 inch tire and why Toyota chose it. For reference, a LT265/70R17 would need almost 49PSI to get enough load capacity. Load range C would top out at 50psi for that size, D would go to 65, and E would go to 80. (80psi would allow 3085lbs in that size). Different sizes have different pressure breakpoints so you have to look them up for other cases.
If you use a bigger tire, you usually wouldn't need as much pressure. For example, a LT285/75R16 tire would only need about 40PSI to be adequate according to the TRA chart. An LT285/70R17 tire would also only need 40PSI.
For reference, here is Toyo's warning regarding LT tires:
"WARNING! Please note that size for size, LT-metric tires require higher air pressures to carry equivalent loads of P-Metric tires and that any failure to adjust air pressure to achieve the vehicle's load requirements will result in tire fatigue and eventual tire failure due to excessive heat buildup. Due to the higher PSI requirements of LT-Metric tires they may not be suitable for replacing O.E. P-Metric tires because of the ride harshness that results from higher PSI."
