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I'd be willing to be that when you factor in the rental fee, plus the one way drop fee for a large SUV, you're going to be looking at a very hefty price tag. In fact, I'd be willing to be that it would be significantly cheaper to go with a small uhaul or similar moving truck. You'll also have a lot the advantage that it should be a whole lot easier to find this kind of vehicle for your trip.
Your route and driving distance look right along the lines of what we recommend - about 500 miles a day. That will put you on the road for 8-10 hours a day, leaving a nice amount of time to stop and taking frequent breaks from the road.