The official recommendation is to run 'P' at one pressure, door card pressure. You might increase the rears a couple psi with towing, but there is very little adjustment available. The other issue with 'P' is that air down pressures will be severely limited. I believe Ronny Dahl's channel has this in video showing some P sidewalls aired down, might want to look at that.
Between those options I'd select the 116 C tire or the JP make 121 E.
Target load for a LC/LX is around 2200lb if I recall.
Yeah, it's a tough balance, the C-rated only have a Q speed rating which is 99 mph. I can easily hit 90 mph on the highway (for example north nevada highways), so would you rather be near the max while hauling ass on on the highway, or near the max while aired down on a trail? i don't know the answer.