I am currently running stock size tires on my Indy. Larger tires or rims will require recalibrating a speedometer usually. There are charts on most of the tire websites.
From what I've been told and what I've read your gas mileage goes down as well. These 5.9 are bad enough as they are on gas, so keep that in mind. On the plus side you will get a bigger footprint so your traction and handling will improve.
Its an expensive choice, but you could always drop/level the truck to make the tires fit the body better. I am planning on doing it when I get done with my interior work. Who knows, maybe it will make the truck a little more aerodynamic.
Whats the condition of your stock SS/T rims??