I'd just tow with the 3.21 and see how it does. Play with locking out 8th or 7th if you have to and find the sweet spot for your speed. Will 3.92 work better? Sure but is it worth it? Up to you.
I think people (especially the 'weigh' police) get their panties in a knot when people go close to their suggested towing capacity. Seriously? The world is not going to end if you are over your suggested trailer weight. Please! I have never heard, read or seen a lawsuit about someone towing over their suggested weight and get into legal trouble, and I've seen commercial hot shot drivers who abide to FMCSA rules/regulations get into accidents above their GCVWR with no legal issues. However, you need to stay within the limits of your equipment. What does that mean? Don't exceed your axle, truck GVWR (this is different than you GCVWR), tire, hitch, and trailer ratings. The tow ratings, which you know are different between 3.21 and 3.92 gears by ~3k# for the RAM, is a guide by the manufacturer to keep their trucks from wearing out within the basic warranty period. We all know a truck with 3.21 gears will have to work harder to get a load moving vs. a truck with 3.92 gears thus the 'recommended' trailer weight.
Do what you want but I wouldn't pay thousands of dollars to change gears or maybe sell your truck just to stay within the recommended tow ratings. The ratings are subjective and fabricated by the bean counters at FCA with input from engineering for longevity not safety. The equipment ratings are for safety. There is a difference. Yes - I'm familiar with J2807 specifications and they are done so a consumer can compare tow ratings between brands that these bean counters have come up with. It is not for equipment failure points and is not a hard 'not to exceed' number. No DOT, LEO or highway patrol enforces J2807 ratings. Case in point - show me where on the vehicle where the GCVWR is labeled? Is it included in the door jam sticker? One would think it would if its so important and 'legal'. Everything else is there (tire, axle, GVWR) why not GCVWR?????
With that said - there is one rating you shouldn't exceed and that is your comfort zone. No matter what numbers you read you should always stay within your comfort zone and personal ability when towing and taking your family on the road. Just because your equipment can take it that doesn't mean you are qualified to tow it if you have little or no experience doing so. Common sense prevails.