Hmmm all of this is great information ........... This truck was purchased new and my dealer installed an Edge chip in it immediately after purchasing. This was done for fuel economy per the dealer's recommendation................... The dealer first said it was Edge and they weren't up to speed with the new programming. They dropped it from 2 to 1. Last week while trying to leave on vacation they walked me through putting it back to stock or 0. Still the same problem. Now they are saying they need to remove Edge completely and put back to stock but what I am hearing is that the problem is the flash from Ford..................Am I correct? Should I have been towing with the chip in 2?.
The problem could very easily be between the flash and the tuner. When you said the truck was stock in your first post, I assumed you meant stock.
I'd look into the model of tuner and see about getting their latest update, and find out if it's been reworked for the 11B23 flash.
I'd also look into the T-stat issue that has solved a few folk's problems.
Oh, and you may want to hand calculate your mileage. My dash computer says I'm getting 24-26 MPG on the highway, but I'm actually getting 17-21 when properly hand calculated. I've never heard of anyone getting better than 22 MPG with a 6.4 when driving it normally (e.g. not downhill with a tailwind).
Regarding your question about towing with the tuner, that's a bit tricky. You really should find out exactly what until you have, and see what Edge recommends for towing. My Superchips tuner (for example) has 5 tunes. #1 is for towing, #2 and #3 are ok for towing up to 6k, and #4 and #5 shouldn't be towed with at all.