The non-adjustable valve train can be noisy, but I wouldn't call these engines "sloppy". Clearance wise, they are just as tight as a modern engine (I use and rebuild a decent amount of Jeep engines, BTW).
I don't think 5W20 would be optimal, but realistically, the engine would run fine. It will most certainly not "hurt" anything. Synthetic started to go mainstream when this engine was new, and IIRC, 5W20 was the offered viscosity.
You would need an accurate oil pressure gauge to determine if it's acceptable. A previous member here ran a custom 0W10 in his Jeep 2.5L four cylinder, which has the same architecture as your 4.2L. His UOA numbers were pretty decent (not that UOA's are the best tool for determining engine wear).
Ultimately, if it's your daily driver, I would play it safe and stay with 5W30. For me, my current off road project is a custom Tube chassis powered by a Jeep 2.5L utilizing a turbo setup (possibly Volvo). I intend to play around with oil viscosities and my sights are set on a synthetic 0W20.