With a GVW of 13,750#, pin weight will be closer to 2700#..more realistic..I had an 03' Chevy 2500 D/A in short bed, extended cab, I don't think that I would have towed the heavy with my truck back then...But I tow in the mountains and has some to do with it. I'm one of those who try's very hard not to go over my GVWR, and buy accordingly....I know quite a few use Axle ratings...nothing wrong with that, but
I feel staying at or under trucks GVWR gives me a lot more safety buffer.
Sounds like you've already made your mind up..I'd weigh your truck already to go, then weigh it again when loaded to see exactly where you are without any speculation.
Jim & Kathy
2016 Ram 3500 DRW/crew cab/long bed/4X4/Cummins/Aisin/4.10/rear air assist. Pearl White
2016 Jayco Seismic 4112, WD/Trav'ler Direct tv SWM satellite, slide covers
B&W RVK 3600 hitch
USAF Viet Nam Vet