For your use type and your experience with Ram trucks w/68RFE.. I am surprised you went the route of Aisin. The 68RFE now has a new valve body and the truck does not feel hindered at all with it versus the Aisin where in my experience, you could not drive without having thoughts about what the transmission is doing or how it is not in the right gear for when you need to pass someone in a bind. I was all about the Aisin until I did more research and test drove. It is very clear the Aisin is a tow pig meant for stock power/factory tuning. IMO if you are looking for a daily driver that is so smooth and figured out that you do not even think about it while driving.. or if you are planning on doing performance mods over stock horsepower, the 68RFE is by far and away the better tool for the job.
I know that when and if my 68RFE takes me past 250,000km's with the proper maintenance but severe use case it gets under my foot, I will not be looking for switch to a different transmission if I have a choice. I know it is too late and you are looking for advice on what to do or tuning for the Aisin, so if I were in your scenario (which I almost got myself into when ordering the truck), I would be dialing back the power even with the fuel economy loss while towing and or doing a manual ''re-learn'' and let the Aisin get some experience in that same situation from the start of the learn process.