Having tuned ECUs before... this may not be what you want to do because the nature of towing requiring prolonged outputs and getting into heat soak constraints. I'm all for turning up the wick as I do in my sports cars, but not for towing.
There's generally two major dials to get more performance: timing and air/fuel
- Advancing timing puts more heat load on the engine and will start bumping into heat soak, octane limitations, and knock. At which point the ECU pulls timing and you're back to potentially worse than stock power output
- Leaning out A/F can make more interim power, but the reduced fuel creates less cooling of the combustion chamber at which point manifests in heat soak, knock, pulled timing and again, potentially less power than stock
There is no free lunch with sustained power and the engine has to be designed for it from the ground up. It will definitely compromise reliability trying to make more N/A power via a tune.
I monitor the stock ECU and transmission and as it were stock, with high towing loads and extended engine outputs in hot weather, the ECU will begin to trim timing and output. Same with the transmission, the more power you put through it, the more heat there will be and even with the great aux cooler and an added aux cooler, can experience heat soak limitations.
Many new to towing assume torque, and drive torque, as that's been parroted all too often. That's only half the truth. Torque (and gearing) gets you off the line. Once at speed, it is all HP. What I'm getting at is that it's important to access the broader RPM. Driving below say 3500RPM, only opens up a bit more than half the power of the 5.7L. There is easily another 30-40% power on tap at the higher RPM ranges. When I'm talking about heat soak with towing, it is sustaining that output, running 4500RPM++ for 20-30 minutes at a time in some of the most difficult grades of the Rockies and Sierras. The 5.7L is up for it, designed for it, and power can be had reliably when using the tool as Toyota intended it.
That said, what are you intending to tow? I tow 8k lbs and the engine makes plenty of power to keep me with traffic, even in major grades. It can also drink a ton of fuel so there is a trade trying to make more power. A better mod may be an auxillary fuel tank.