Trying to understand normal tow handling

The GVWR is actually 7100 for the R/T AWD. The payload capacity of 1380 includes the driver and a full tank of gas

Not saying you're wrong, just can't find the driver included info anywhere. Normally the "tow" rating includes 150lbs for the driver but "payload" does not. Maybe Dodge changed that? Payload is simply GVWR - curb weight.

Be careful using the factory specs too, delivered models can vary significantly in weight depending on options. The best thing you can do is test drive the vehicle you want with all your passengers and drive over a scale. Your loaded weight subtracted from GVWR is what you have left for the trailer tongue weight. If you're under then you should be ok, assuming you are also able to stay under the axle, tire, and receiver ratings.

Also, don't forget that the tow rating decreases pound for pound as weight is added to the tow vehicle (apart from the 150lbs allowance for driver). If you add 1000lbs to the Durango your tow rating drops to 6250lbs (7100-1000+150)

I still think it's going to be tight and the money you will spend to "upgrade" isn't going to get you the comfortable towing experience you are looking for. Being at max or over isn't fun.

I came from a similar setup. Toyota 4Runner V8 towing a 26' bunkhouse that weighed 5500lbs loaded. The 4Runner had 1300lbs payload and a tow rating of 7100lbs, very similar to the Durango. We were well under the GCWR and tow rating but right at the limit of payload (with only my wife, 2 small boys and dog). It was a handful, 2 hands on the wheel at all times. White knuckles in winds or big trucks passing. The short wheelbase, high center of gravity and soft P rated tires were some of the issues. I upgraded the tires and used a $3000 Hensley Arrow hitch which improved things a bit but it was never comfortable. I lasted one summer before buying a truck. Just like the other post with the Durango looking to upgrade.

It's good that you're doing your homework now. I hope you find something that works.