I have a 2012 with the same setup currently, 6" zone lift with 35x12.5 on 3.55. I've heard numerous people tell me to do the gear swap because it'll save your tranny but I'm still hesitant on it because it costs so much. I don't have a problem with my, yes it uses a lot more fuel, yes it doesn't hardly go into eco, but as far as I can tell its fine.
I've been to two shops and they say 22oo installed. Is it possible to do it yourself? I've heard the gears or something has to be drilled by a machine shop or something?
And Brandon, what's this about swapping the front diff? No shop has told me I had to do this. They said it was just a simple swap.
The fuel economy you end up getting all depends on where you're doing most of your driving. If you're on the highway a lot changing gears isn't going to get you better mileage, it will likely be worse. However in the city it will do slightly better with all the stop go traffic. All in all in generally ends up being a wash and you'll be getting about the same that you are now.
Unless you've changed gears on these types of differentials before I would highly recommend getting a shop to do it. It can be done with some guess and check methods for the average backyard mechanic that knows what they're doing. It's a pain in the butt but you'll get it right eventually (provided you have a few of the key tools needed). But a shop does it with precision tools the first time. Not to mention they have the experience with setting up bearing preloads, backlash, etc. Gears installs are not something you want to screw up. If it's not done right the gears are often shot and will need to be replaced before they can be setup right again.
On 2012 and up trucks the front ring gear is welded to the carrier so it cannot be changed. You need a front diff from a 2011 to actually be able to change the gears. This will up the price above $2200 for sure.
Depending on the size of gears you want to put in, machine work on the differential housings may also be required (for 4.56 gears for example).