Welcome to the Z, John! Sounds like you have travel plans!
Let me see if I can't help some.
I tow with a lifted (4") Ram on 35's. I always try to go with a load rated Class D or Class E tire. With your load, a Class D tire should be more than sufficient.
Since the rear suspension on the generation Ram you are considering will be a live axle with leaf springs, your lift there will be a set of blocks between the leafs and the axle tube with extended length U bolts. One option is a good set of air bags at the back to level the load. You could even use air bags vs. blocks to raise the rear.
You will need a drop hitch so that when you hook up the trailer it will be level vs. running downhill, front to back. I just measured my trailer hitch height with the trailer levelled, then measured to the center of my hitch receiver, then took the difference between the two. That is how far the ball top had to be below the center of the receiver tube.
Shudder should not be a problem as long as your truck remains level while towing. I have no problems with that condition because the loads I tow don't compress the suspension enough in the back to raise the front end much. Again, levelling the trailer on the hitch and possibly using air bags at the rear to level the truck should eliminate that problem.
On the tires, look for the proper load rated tire. Here's some links to those load ratings for your info. In the second link, look at the Load Index info.
Any good tire shop can hook you up with the right tires as long as they know some basic info on the weight of your truck, the weight of your load and the tongue weight you will be towing.
As far as tires, I have towed heavy loads before (5'vr) and I got really good service from the Toyo M/T and A/T tires.
The differential gear sets you are discussing seem a bit high, numerically, for what you are going to be doing with the truck. You do need gears higher than 3.55's but a 4.56 is a bit extreme unless you plan on towing very steep grades off-road. I'd suggest no more than 4.10's and I believe that a 3.92 set front and rear will do very well. You do have to tow on the road and really high gears will kill your mileage with little additional benefit.
I'd strongly suggest you move up to a HEMI in a 3/4 ton or even find a clean used diesel Ram, especially one with a 5.9L 24 valve Cummins. They are tow monsters!
My only comment is to pass on the Jeep transmission. They were not built for a lot of towing and the diesel Ram's have all you need with respects to towing as they are geared properly and are built to tow.
Good luck with your choice and holler back if you have more questions or want to discuss this further. We will be glad to help.