I wouldn't with the 37s for the risk of burning up the transmission or other transmission wear/damage. Although towing to a 9,100 travel trailer and commercially for 475,000 miles now I will say the 8 speed is tough. (no issues knock on wood) Dramatically better that the by comparison junk it replaced. Naturally you can watch your trans temp as well as coolant and oil temps which could be acceptable at lower speeds with no long grades but only experimentation would find out and for how long. Certainly Ram would tell you no and not warranty it. Also you can change your transmission & differential fluids afterwards if you do run them into red temps for very long. But don't run well into the red zone for trans temp for extended time or you run a serious risk of fire.
Now if you can throw on some factory rims especially 17s with say a 33 or better yet 31" load rated tire then their should be no problem in that area.
Personally I don't care much about exceeding GVWR in fact often for larger loads I set them up over GVWR when I wouldn't have to in order to get the more important items such as tongue weight and axle weight distribution all withing spec and in balance so to speak for my priority of the safest and most stable setup. In order to find that you have to take it to a CAT scale. I realize this isn't always practical just saying. If you want to tow that safely and at speed you need to prioritize getting your tongue weight in the 10 to 15% range ideally normally 12 to 13% of gross trailer weight. Then you should have no sway issues even when windy and at speed especially if you additionally have a WDH with built in sway control. Also you want to replace your unloaded trucks steer axle weight and keep your drive axle weight to its limit when loaded with trailer and unimog so that your truck handles with stability and full braking power.
People with little actual at limit experience towing who have never taken a dangerous to drive and stop "white knuckle" over spec setup to a safe stable within spec setup only by changing the weight distribution with no weight loss talk about payload. People who know how and have done it talk mostly about tongue weight and axle weights.
The 1500 platform can be made to control to an 8k trailer well but beyond that you generally get into having more weight on the trailer axles than on the truck axles and the bad side of the laws of physics when things get pushed due to other traffic, in-climate weather, downhill sweeping curves etc. When I took the 9,100 pound 36.5" ball to bumper box travel trailer 1,000 miles over 5 & 6% grades on the 5 past Cali's Mount Shasta and up the grapevine into LA the only benefit my 14 1500 had over yours was the tune provided turbo brake from the Ecodiesel for assistance controlling speed down grades, and good axle to frame airbags. Naturally assuming you have a properly sized no sway WDH.
ughts how well it might do?
