For all the Max indicated versus Less discussion, I'm not sure I saw anyone suggest running the TT's tires at what the TT manufacturer suggests. OP has a brand new TT and I'm willing to bet there is a sticker that specifies the tire details (size and recommended pressure).
In my case since my TV is an SUV, I run those tires at what the mfg recommends when not towing (for better comfort and performance, however you want to measure). But I run the rears up near the sidewall rated max for towing since they're not LT's.