Pathfinder III
Trailer mounting isn’t and option. I tow boats, not those little off-road overland trailers. I pull the bass boat in my profile pic all over the southeast. I also have a center console I charter in south Florida. So the spare need to stay on the truck.The OP does mention regearing to 4.10.
I don't see the point in spending $3000 to regear, and then settling for just 4.10's. For perspective, the F550 I drove last week had 4.56 gears with the stock size DRW tires. Don't fear the gear. It might be worthwhile to research what Dodges 4500/5500 are using for gears.
Now that I read that you have a trailer involved, I recommend modding the trailers to have a mount for a 37'' spare. Put your trucks spare on the trailer instead, keep a 35 in the stock location. If these trailers are large, I recommend dropping down to just 35'' tires.
I wouldn't use a hitch mounted carrier, if I was towing more than 2 jet ski's. If the 37 must be mounted to the rear of the truck, I'd go with a custom bumper that holds that tire very high over the bumper. Based on the assumption that your trailer is even, or lower than your rear bumper. Can hang off as far as you need, if it's over the trailer.
If I go the travel trailer route, I'm adding another tire carrier to the rear bumper of the trailer.
I did mention rehearing yes. I say I will be regearing, not “should I regear?”