First of all, you can't use the dry weight of the trailer - there's propane, battery, water, gear, etc that you will be traveling with. The dry weight is the weight from the factory before anything is added to it. No one travels dry.
So let's assume you travel light and add a mere 700 pounds to that dry weight, for a total of 3500 pounds. Assume 12% tongue weight (12% is standard) and you'll be around 420 pounds tongue weight. Now add maybe 400 pounds of human weight, 300 pounds of stuff in the truck and you'll easily be around 1,100 pounds of payload.
Does your Tacoma really have 1600 pounds of payload???? That amount is better than some 1/2 tons.
So with that, I think 1600 of payload capacity is acceptable (however, I do not believe your Tacoma has enough power to adequately pull all that or enough braking capability to stop all that), but it all depends on how much you pack and how many passengers you have. I would definitely be looking at 1/2 ton trucks and the Tundra is a fine truck for that (but they do suck the gas).
FWIW, I get about 14-16 MPG (combined) in my 5.3L GMC Sierra. I can get in excess of 20MPG on the highway. About 10-12 towing.
Good luck with your search.
Palomino SolAire 307QBDSK
2016 Chevrolet 2500, CC, 6.0L, 4.10