I just bought the exact same truck, except crew cab. I traded in a 1/2 ton 2010 Titan. I experienced the same situation you did with slowing down, downshifting and high rpms going up steep hills (picture I-80 between Sacramento and Reno). My trailer is a Jayco 29RLDS, so a few more pounds than yours, but not much.
I occasionally had the tranny temp on the Titan go up on uphills and had to downshift and slow down to get it back to normal. (The Titan had the full tow package, BTW.) I also, more importantly, was at the limits w/ weights and WD, and had braking issues. I experienced loud clanking noises from the front end in a hard-braking downhill sharp turn!! (At relatively slow speeds.) I also had to turn warped front rotors at only 32,000 miles!
All in all, much as I loved my Titan, the 2500HD is a real truck, and you will find that ease of towing and safety are more than worth the upgrade. The exhaust brake alone is super.
(I had 20" tires on the Titan too, and I believe it's more for mileage than anything else. Yes, they would cause a downshift on hills sooner, and you won't get out of the hole as quick, but I assume you're not drag racing. You won't notice an issue with the 2500HD, except better mileage, which I'm already getting vs. the gas Titan. (12 towing vs. about 8 w/ the Titan.)
Jim