I'm not concerned about the gears. Even if all the numbers work and you stay within specs, you'll be close on all your numbers. In my experience, you'll be fine but you'll be limited on how far you tow and how long. And being in mountains, well that would be a big limitation. I've towed two different combos close to my limits. Its worked fine in the flats of WI, but I would never have taken either of those combos through the Rockys. That said I think you'll hate it. I'd be looking at trailers at least 1000# lighter.
You also said "family". How many? Keep in mind the kids grow and so does the amount of stuff they bring. Today you might keep within the payload numbers. Two years from now you might be over. Something to think about.