For my '06 LJ Rubicon with 4.0 motor I use:
Valvoline Maxlife 10w-30 synthetic blend motor oil
Fram Tough Guard oil filter (P/N TG16)
Change Interval every 5,000 miles or 6 months, whichever is earlier
To OP:
My inclination, regardless of whether you elect to use synthetic, synthetic blend or conventional motor oil would be to start with a 5,000 mile / 6 month change interval then send a sample to Blackstone Labs for testing. Blackstone's analysis typically includes their recommendation for a change interval based upon the specific findings for your oil and engine.
The Blackstone Labs test has two primary benefits: (1) It will give you an idea of the condition of your engine based upon the metals and contaminants found in the oil; and (2) The results show the condition of the oil and its additive package which will allow you to determine the optimum oil change interval theoretically saving money over the life of the vehicle. I test once each year per vehicle. Its worth the $28 to me to know rather than guess based upon the color of the oil in the drain pan. YMMV
The odometer on one of my vehicles just passed 138,000 miles, the last 40,000 of which using Valvoline Maxlife 5w-30 synthetic blend motor oil. Blackstone has recommended that I extend the change interval in that vehicle to 7,500 miles then re-test.
I haven't had my current jeep long enough to collect enough lab data to evaluate oil change intervals. ['06 LJ Rubicon.] I changed over to Valvoline Maxlife 10w-30 synthetic blend motor oil, and will change it every 5,000 miles or 6 months, whichever is earlier, until I see test results that provide a compelling reason to vary from that schedule.
I see no point in using full synthetic motor oil in the Jeep 4.0 engine. The "severe duty" maintenance schedule calls for periodic oil changes regardless of mileage. Since it is unlikely that one will reach the specified change mileage before reaching the specified change time, there is no advantage to paying extra for high mileage synthetic motor oil.
See:
https://www.blackstone-labs.com/