Most Ford dealers and Independent axle and 4x4 shops can do the gear swap. You do need to have the ECU reprogrammed, which can only be done at a dealer (as far as I know).
The gear swap should run about $750-$900 depending on your local labor rates, and then reprogramming the ECU is 30 minutes labor.
While you are at it, you may want to to consider an ARB air locker or and electric locker for your rig, considering it's weight and where you may be taking. Not cheap, but having 2 open diffs means you really only have 2wd still (one on each axle) and Limited slip can be good (other than Ford, which doesn't have enough pre-load) but I've discovered that with my heavy setup, I'm seeing much more clutch wear than I expected. Enough so that I have to periodically clean my differential speed sensor because it collects the clutch material. My van is around 8000 pounds on the rear axle when loaded, which I imagine is similar to your rig.
You can get a Powertrain Control Solutions standalone controller from http://destroked.com/
. But I think you may lose some other features (like Tow/Haul mode).
I strongly suggest the gear swap before doing anything else. With the 4.56 gears I rarely turn OD off, except for braking, which your Tow/Haul mode does for you. BTW - you should probably drive with Tow/Haul most of the time. It will reduce hunting.
There is a product for the E-series which will default to Tow/Haul mode: