I'm also in Colorado, familiar with the trails you're talking about and the roads to get there. I hope this long form post will help you and others think through the why of your specific needs. The decision factors are different with other transmissions or engines. Ie with the manual, 3rd, 4th and 5th are closer together providing other gears to get into the powerband. This tool is helpful.
https://www.grimmjeeper.com/gears.html
The main issue that can damage your jeep's mechanical system is low rpm - high load situations on the motor aka lugging, a combination which isn't great for any motor, especially this very old architecture. If you your cooling system is not in tip top shape - this could quickly get you into trouble and end your trip. Much more important than gears, but gears get you out of this situation too.
The gears won't make as big a difference in the offroad side of things for this trip and you won't break anything on those trails specifically due to your current gears. Gears are much more about managing the on-road performance with any vehicle that has 4-Lo, though they'll still provide benefit in 4-lo.
Your tire and gear combination will absolutely perform better on road with numerically higher gears. Peak torque on the TJ (4.0L) is at 3200rpm and peak hp is around 4400rpm. You don't need to be cruising in overdrive in this range, but because of the wide gear spreads between gears in the auto you'd want 3rd gear in the auto to get into this rpm range in the speed range from 60-75 mph or maybe 55-70 mph depending on personal preference. One issue with the later 4.0L engines is the very mild cam, long intake runners and small exhaust ports don't breath very well above 3500rpm, torque falls off and it doesn't increase power as much as you go higher.
Assuming your tires are currently 32" actual diameter (they'll actually be 31.5 or so) and I believe your vehicle runs the 42RLE transmission,
engine RPM with 3.73 in 3rd at 60mph is 2350 and 75 is 2937 with OD at 75mph at 2027.
engine RPM with 4.56 in 3rd at 60mph is 2873 and 75 is 3591 with OD at 75mph at 2478.
engine RPM with 4.88 in 3rd at 60mph is 3074 and 75 is 3843 with OD at 75mph at 2652.
engine RPM with 5.13 in 3rd at 60mph is 3232 and 75 is 4040 with OD at 75mph at 2788.
Both 4.88 and 5.13 will give better alignment between the engine powerband, your tires and our roads and work with the very tall OD in the 42RLE. If your tires actual diameter is at or lower than 31.5" and you don't plan to
ever go up to a "33" - the 4.88 ratio would be a little better I think, but others differ in preference. If you want the power to come on closer to 55 mph or think you might go to a 33" tire in the future then the 5.13 would be better but be aware this could put you in a quite high rpm on the 85mph speeds on the interstates in neighboring state to use 3rd gear effectively.
I also agree with others - if you're considering a Dana 44 rear axle - now is the time to install it. Lockers? Now is the time to install them. Do not do this twice.
There is no free lunch as the higher numerical gears will also spin the driveshafts at the higher rpm. The rpm in 3rd with your transmission is 1:1 and gives you actual driveshaft rpm at a speed regardless of gear. This higher rpm increases wear on the driveshaft joints and if there is any imbalance may bring that down into the range where you encounter it in normal driving.
If your X is a 2005 or 2006 you also need to make sure to update the speedometer gear or use a speedohealer to correct the speed signal fed to the PCM because these years jointly control the engine and transmission shifting based on the vehicle speed input along with other load factors. If you have a 2003 or 2004 X then you should still do this, but the transmission and engine ECM management are not linked. One of those reasons being the 03-04 have a hard fuel cut speed limiter at 92mph indicated which you'd reach at a much lower speed with 5.13 gears.
