What you are experiencing is nothing new, well not to those with an automatic and towing a heavy load. Your description fits the classic signs of early transmission failure. The TC and perhaps a clutch pack are slipping under the strain of the load. Empty it runs just fine, for now anyway. Give the whole thing a few more miles under load and then you will start to feel it slip while UN-loaded. WHY??? Because the Dodge automatic transmission is a week link in the drive line. Yes it is a good and tough transmission for gas engine use, but no matter what Dodge does or says they do, it will never be strong enough for constant high load diesel use. There are many reasons why, wrong stall on the torque converter and not enough friction area (clutch), Low oil pressure system, week clutch packs and bands, the list is almost endless. Yes, there are many aftermarket companies that can take your 46,47,48re and transform it into something that will live and outperform the stock unit. But it is also not cheap, average cost somewhere around 5-6,000. Not a bad price for what you get in re-turn, but a hellof alot of money for someone that just paid 40K for a new truck to cough up. Bottom line is Dodge has had there head up there rears for way to long. Most competitors (Chevy, Ford) have invested the funds necessary to make a modern day automatic work and work very well bolted behind a modern day diesel. The old Dodge automatic that has been around since the 60's is simply out-dated and over stressed in a diesel pick-up. Personally I find the Ford 5-speed auto to be the best HD automatic offered today. It shifts smoothly and works great pulling a jet ski or a 40 foot GN. Dodge is reportedly working on a new and better auto, but then again I have been hearing this for the last 4-5 years.
What can people like you and me do? If your truck is still under warranty, and if you haven't done anything to jeopardies that warranty(power adders), then I suppose you could keep letting Dodge replace the trany as long as they keep doing it. This does nothing for people that need there truck everyday for work or business, and installs little confidence for the vacationers. If your truck is out of warranty, I would strongly suggest going with a aftermarket trany, or selling the truck. Investing money on a Stock trany rebuild, is a pure waste of funds. So is only going half the way on new pieces. Many feel like they can replace the valve body or TC and the problems will go away, wrong! I would suggest total replacement or trade.
One of the best investment anyone can make that owns a automatic diesel truck, is a auxiliary transmission cooler. The cooler the fluid the better. Normally on the open road the trany's stay cool enough to be safe, but in hilly areas and in city or stop and go traffic, the temps go up very quickly, and remain there. When the trany does slip, it creates a huge amount of heat, no surprise friction always causes heat, but slipping parts cause extreme heat. Same goes for when a clutch on a manual tray slips, it takes very little time to destroy a pressure plate and flywheel. Anyone towing should consider a cooler, but anyone towing over 8000lbs it should be considered mandatory. Coolers alone won't make up for all the troubles associated with the Dodge automatics, but they will help them last.
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