Load E tires and airbags will get you mostly there. Late model TRD Pro have the same max payload capacity as my 2013 Tundra 4.6. The primary difference is mine is a DC with 6.5' bed and your Pro is a Crew Cab, so your payload will be sitting 1' further back on the chassis. It's not ideal, but if you drive conservatively, it will get you by. There are others that have CAMP-X in crew cab fullsize pickups. All Fullsize pickups need to be driven with care/caution when loaded right up to max payload. We just got back (literally 30 minutes ago) from another 24 hour overlanding trip through the mountains. Nothing too crazy but to give some point of reference, on most of our trips while on the forest service roads, we probably spend 1 out of every 5 hours in low range 4x4. I'm still impressed with how easily the Tundra handles the load, though in all honesty, I would be even more comfortable if our rig was an HD. I like having a cushion in payload for unexpected situations when out on the highways which are the main times that I feel an HD would perform better (curves/lean and emergency braking). That being said, driving smart goes a long ways.
No one seems to know exactly when the new Tundra will hit the ground and be available. Anxious to see those details myself. Fingers crossed for a "heavy half ton" option on the Tundra. Us pickup camper users don't need huge, gas guzzling HD engines and towing power (I'm super happy with out "little" 4.6 liter V8); We just need payload capacity and appropriate braking capacity to support that payload; don't need braking capacity to slow down 14,000lb of trailer. Ha. I'll be looking for a new truck next year and trying to decide between a fullsize and HD (and will consider all the options like re-working/re-springing suspension on a fullsize). The big consideration for us will be if, sometime during the lifetime of the next pickup, we change from a CAMP-X to a CAMP-HBE which, in my opinion, would sway us over to an HD unless a very capable fullsize package comes along since I don't see any now.