One thing to keep in mind is what kind of JK it is. A lot of people I wheel with got tired very quickly of being high-centered while running 33-35" tires on their JKUs; The 2 door guys seem to do better with 35s. The issue here is that running 37s on the TJ/LJ/XJ platform was a huge deal, usually costing the owner drivability or a lot of money.
Running 35s on a JK is no big deal and 37s are also way easier to deal with on the JK than on the TJ/LJ/XJ. You're ahead of the curve with front and rear Dana 44 axles.
The type of tire is important also, Nittos will be way heavier than a Goodyear MTR/K and they'll measure up differently too; a KM/2 will run smaller than an MTR/K or a Nitto.
As for gearing, you need to look at it from a cost benefit perspective. While you might get a few more MPG swapping your R&P, is it worth the cost of doing so? Expect to spend at least another $500-600 in parts alone for a re-gear.
I wheel with guys that run 35s and 37s on 3.21 and 3.73 gears and they do just fine. I would run a 35 or 37 inch tire on 4.10 gears any day. (this next part is typed from memory of a thread on Jeep MPG a few years back so excuse any mistakes) The 4.0 engine does not like to be lugged, and does better on gas above 2300 RPM, where there is enough gas being injected in the cylinders to cool the walls. Under a certain RPM, the computer dumps fuel into the cylinder in an attempt to cool it down, causing not only a drop in MPG, but also richness of the Air/fuel ratio. The JK engine doesn't deal with that same problem, so ostensibly, shouldn't be that affected by being a bit low of its target RPM.
When actually offroading, your 4:1 transfer case and lockers work to hide any deficiencies your gearing might have. One of my friends has a Rubi Unlimited, with the stock 4.10s and 37 inch MTR/Ks on ATX Slab beadlocks, not exactly a super light combination. He drives it daily, gets pretty respectable gas mileage, and is extremely capable offroad.
Just something to keep in mind.
