Is this a 6 lug 2500, or the 8 lug 2500. 2600 lbs of payload seem pretty low. unless it is highly optioned for an 8 lug. I have 3800 with my same body style 8 lug 2500. If a 6 lug, you probably have or had stock a 6 ply LR C 245 tire on it. So going to a 10 ply 225 would not lose too much if any tire load payload. Another route to give you a skinnier tire, same OD is a 215-85-16. I used to run this stock size on the rear of a dually, and 245's on teh front, no issues with the 4wd system. As both were sized at 30.5". Even the psi and weight on a given axel can change the active diam which is more important than the rated diam.
2 Get new tires, then alignment....
3 Shocks? how good are the springs literally? If a lot of miles, loads etc, they may be worn out, a new set of springs could be a good thing.
Marty