My 4.2L 5-Speed Manual (converted to 1994 4.0L fuel control system with fuel injection) failed as a gross polluter in California. Had a new Catalytic Converter welded in and it passed with flying colors.
I assume your "Check Engine" light was NOT on and no malfunction codes exist in the computer.
Does AZ require the fuel tank to be pressurized, looking for evaporative leaks? California does. Take the Jeep in with a FULL fuel tank to GREATLY speed up this test. Should not affect HC and CO though.
Many people believe that running fuel injector fluid in the fuel tank helps clean injectors, and it MAY if they are "not-too-dirty ". I occasionally pull the injectors and clean them individually. Remember, though, that most fuel additives do affect combustion and put degrading stress on the Catalytic Converter. Clean Injectors, a new distributor cap, rotor AND quality spark plug wires greatly helped my hesitation issues. Under heavy acceleration from a stop, do you detect a "miss"? This often is caused by old or cracked spark plug wires or a dirty distributor cap with internal lines of carbon arcing.
Use a quality fuel. I don't want to start a argument on this forum, but I've seen evidence that using the most inexpensive gasoline results in excessive intake system carbon buildup, especially on engines with EGR systems. Costco gas is the worst. AND, use the proper grade. "Regular" should not be used, primarily for detonation concerns. Octane rating does not affect fuel mileage. I prefer Chevron... I believe it actually does burn "cleaner". Check your throttle body for cleanliness.
An obvious issue that I only mention because I don't know your maintenance regime, is spark plugs. Pull them and inspect for cylinder issues such as oil burn, overly rich, and gap. Always go with new plugs. Gap them yourself... don't believe the "factory pre-gapped" claims.
Here's another oft overlooked recommendation... make sure your thermostat is working and that the proper coolant temp is maintained. In the world of emissions, cooler temps are not always good. I use a 195°F thermostat, required by my "California Approved" EFI conversion which uses a standard 1994 Mopar Jeep 4.0L computer. Operating cooler is detected by the computer which operates in a less efficient mode (including timing) until it "sees" the correct higher coolant temp. By the way, how is your coolant temp sensor doing these days. This is another often neglected component.
Crankcase Ventilation can suck excess oil from under the valve cover into the intake manifold system. Inspect and clean accordingly. Also, keep clean oil in the crankcase.
Change or clean your air filter before you retest.
Not knowing anything about the condition of your Jeep, my instinct is that you will get the most bang for your buck by replacing the Catalytic Converter.