I don't know about Mobil 10W40.I just advise against the Mobil 1 10W30 because the UOA's I see here show much higher wear rates than almost anything else,and every 4.0 I've heard that ran it sounded louder than normal.
You could do the T&SUV 5W40 if you want to spend the money.
I used the regular Castrol 10W30 for my 4.0 when I lived in NC, Regular Chevron 10W30 after I moved to Seattle, and for the past year the HM 10W30. You might not find Chevron in FL, but Havoline is about the same, though Chevron says it's a bit better in the add pack.
If you look through the Jeep 4.0 UOA's you'll find some good stuff.
I was impressed with aztec's UOA on Valvoline Maxlife, which was the best I've seen on this engine.
The HM has cST of 12 @ 100, while the regular sports a 10.8. The 10W40 regular is 14.8, so as you see, the HM is a good place in between. Starts out with a higher Base number as well, 7.9 rather than 7.4.