My 2c is you're looking for a reason to upgrade (not that that is a bad thing).
The steelies on your truck will support the load of some better tires. Yes you'll have to get taller to get significant load rating increase but you're getting taller with the 245 19.5s too.
Seems 18s and 20s have more high load tire options now and takeoff OE wheels are dime a dozen. Like just got a set of stock Ram takeoffs 3750lb cap. Brand new $1000 Craigslist special.
IMO that would be a good economical option.
Regarding the gasser and gears, I've pulled/hauled around the equivalent of your camper and then some both with the 245 donuts and 285/70/17s and IMO it wasn't noticeably more gutless. You got lots of gears to choose from on the shifter. It's not going to pull 5th or 6th up a hill and probably not 4th either when you're loaded down even with small tires or lower gears. I'd keep the re gear money in my pocket book not in the differentials. The engine is made to rev and is kind of sickly at low rpms anyway.
My 2 company trucks, a 2013 and now 15 model identical to yours have been flawless mechanically and good tow rigs save for needing to wring them out when pulling up hill.
