We've done both ways, but generally have gone the trailer route, especially for long moves like this. When you're talking about being on the road for 6 days, having someone to talk to, point out thing you might otherwise miss, and yes, even share the driving is nice to have. Usually the trailer doesn't end up costing more than what you'd spend on gas for the car, so towing would be the way I'd probably go in your shoes.

AAA won't really be of much help, unless you are driving your own car. UHaul/Penske/Budget will be providing your roadside coverage if you are in their trucks.