Just my opinion, however, in the end, I dont believe you will be happy spending that much money to go from 3.73s to 4.10s. I'd go to 4.30s minimim, or 4.56s with stock tires. If your worried about your warranty, if you have the work on the diffs done by an independent shop, the warranty on those will be toast if they discover the regear was done by a 3rd party shop. I think around $1,500 per axle all in, is the current rate, but shop around. Cheaper isn't always better but you probably already know that.
I've heard of folks who test drove a 73 and a 10 geared truck back to back and couldn't tell any difference. I wont get into why you want to tow a nearly 10k trailer at 70 plus mph and all of the potential consequences of doing that here, you are probably already aware and have made the choice to do so, but I wouldn't suggest it as a general practice for others reading this thread. Its been covered at length several times before in the towing section. At nearly 10k loaded your on the edge of Cummins territory, especially with a 6 speed truck, so towing performance will be reduced at those weights.
If your set on the 10s, I agree that finding a good independent 4x4/jeep shop is best and one that has done a few Ram diffs in the past. You'll get better work and a better price than the stealership. Most dealer techs these days are parts swappers who don't set up diffs regularly and if you dont have them right they will be noisy, or worse, go bang. I suggest you use AAM gears also, they built the axles in our trucks.
Good luck with your decision.