I tow with much taller tires than that, and although I do have an intercooler, you can do much better than what you're seeing if your truck was acting right. As was mentioned above, rpms are crutial. I don't even think of towing heavy under 2500rpms. I like to run 2600-3000rpms depending on load and the speed I want to run.
As far as the "other" things go, number one is ICP and number two is timing. If your ICP is bogging down to lower than 2000 at least, combined with very mild timing, and rpms and boost being too low, you can easily get hot quick.
Injectors are far from your problem though. Give old ****** a chance, the towing I'm referring to was with 250cc hybrids so injectors don't just "make" something run hot. Bad surrounding conditions do, like timing, ICP, rpm, boost..........
You'll get it I'm sure. I would highly recommend losing the fear of an intercooler though if you honestly plan to tow regularly on any significant weight at good speed without water, or a different charger, or something much more expensive than an intercooler.
Good Luck