I wouldn't worry about any trucks GVWR. Hell 99 percent of trucks operating commercially do not use the trucks GVWR to determine axle/tire loads. Nor does our trucks have a sticker GCWR. Weak link/safety issues with a 2500 can be lower rated tires/wheels and no aux upper overload spring pack. Your bags take care of that issue
As other say tires are a weak component along with the OEM wheel ratings. With a 6010 RAWR it does no good with a tire at 3195 and the wheel has a 3050 ? lb rating.
The rear axle itself is the same AAM 11.5" used on the 3500 SRW and DRW trucks so its not the least bit stressed.
If you like the batteries I would upgrade wheels and tires to a higher capacity. Some one will be along pretty quick and say just put 19.5" tires and wheels on your truck...which is a great upgrade. For more input on 19.5" 4000+ lb tires/wheels check out our truck camper forum where its a popular/safe upgrade for 250/2500 and one ton SRW/DRW truck owners who need more capacity.