Although it is easy to set up your own shuttle, there is a lot to be said for arranging with a commercial shuttle service. All you do is drive to the put-in, rig up and go! Sometime during your trip, the commercial service will come and get your car and drop it off at the takeout. Perfect!
The price is more expensive than arranging your own shuttle, but you save on time and hassle.
But be forewarned! Moab is now pretty much a year-long destination. The shuttle services get very busy carrying people to-and-fro for all the fun things that there are to do in Moab. If you need them to shuttle your car, contact them early to make sure they have capacity for you.