I've towed 2k~ lbs over my tow rating with our '01.5 250hp Cummins powered auto/3.55 2500HD Ram and 11,400 lb 5th wheel. Like said above, it's a HP issue, not a weight carrying issue. Around the relatively flat southeast, we did fine and the occasional grade like Monteagle Pass wasn't a problem. What limits the tow rating is startability up a grade, not climbing the occasional grade at speed. In my case, I didn't nor would I exceed any weight ratings but, identical Rams with shorter gears were rated to tow 13,400 lbs so for us, it was a simple performance issue. I never had to launch from a dead stop up a steep incline so we never noticed the difference.
Upgrading the truck would likely result in better sleep if nothing else. :B