4.0 is a beast. I have had 2, would have another one if it was available in my newer Jeep. I used everything in those without any issues, conventional, blend and full syn's of various brands. After about 120,000 it seemed to like Valvoline Maxlife conventional the best. Any decent oil done at proper OCI will should put the 4.0 well over 200,000
One thing to consider is the 4.0 is notorious for having a weepy rear main and I saw a little drippage when using a full synthtic, as my rear main needed to be replaced. Blends and conventional were fine though.
I ran 10-40 in summer and 10-30 in winter. If your rear main is intact, I would use PP full syn. If not, then I would run a good conventional at the appropriate weight.
Side note: I have a friend with the 4.0 in two Jeeps, he did UOA's on them last year with M1, and switched to PP due to concerns about the iron wear.