tires

it sounds to me to be a tranny issue, not an issue with the size of the tires. your rpms will average a little higher because of the larger diameter of the tires, but not 4-5000. i have 37's on my truck and going down the highway at 75 my rpms are at 3000.

Generally larger tire diameters reduce engine RPM... If it's going up it means something is slipping... I'm guessing you have an auto... There are a handful of things that can be done. Easiest is to put a more appropriate tires size for your drivetrain on. Next to that I'd look at either a replacement or kit to bring your rear-end ratio higher. I don't know whats available for your truck so you'll have to do some searching, or I'd try asking on a ram enthusiast forum, maybe they know a flaw with your vehicle I'm not aware of, but it sounds to me like your slipping due to the increased load and rotating mass. Good luck.

The larger tire is like swapping in a lower numeric rear axle ratio. (Example 3.55-1 to a 3.23-1) That puts additional load on the transmission which could put a marginal clutch pack over the edge of slip tolerance. Could also be the Torque Converter clutch. The TCC on my 01 found it's limit when I hooked up the trailer the first time. New converter and trans overhaul cured the problem almost 100K miles ago. Remember the TC and trans are the link between the power and drag. It is the component along with driveshaft and u-joints that is fighting between the pull forward and hold back.