I have just been doing some interesting reading on oil and oil filters in this forum. From what I have just read our oil pressure problems can be caused by a bad or defective oil filter!
Try changing your oil filter and use a different brand filter than the one you have now and see what oil pressure you get.
Also, what brand oil filter do you have on the jeep now?
From what I have read, some filters can cause excessive pressure loss through the filter. Some reported a 10 to 30 psi pressure drop

from these filters that was elliminated when they replaced the new filter with another filter (usually a different brand). It is not clear to me yet whether it is a just a case of a defective filter (internal defects of some kind), specific brands and part numbers causing the pressure drop, or a mixture of both. :dunno:
They also reported problems with the anti-drainback valves in certain brands that lead to engine wear in the early seconds of engine starting!
Search "motor and oil and filter" in this forum for intersting reading and more details if you want to know more.
I am planning to go buy a few oil filters (different ones) and run some oil pressure tests and start up pressure tests of my own after what I read.
I will start by getting rid of the Quaker State (turns out it is private labeled Fram) oil filter I just had installed yesterday.
Mike McGinness
South Houston, TX