Don't try to take a car rental 4x4 on Moab's trails,
The OP did NOT say WHICH trails they want to drive on. I've been to Moab and there are plenty of trails which can accommodate a "regular" rental. Heck. I even took a 2WD rental car on a lot of the regular dirt roads which meander behind Arches/CanyonLands.
Until we know WHICH trails the OP wants to drive on, then I think it premature to state that you need a fully prepared Jeep.
The rental companies have never had a problem with taking a rental "off-road" - I've never abused/damaged any vehicle under these circumstances.
An alternative to a Jeep is a RAZR. I've rented ATVs and dirt-bikes out there - had a blast each time.
G