What would be an estimate of what a shop would.

We don't get involved with costs here because there's way too many variables. Besides, if all that is wrong is it slips in reverse, you need a proper diagnosis and a repair, generally not a total rebuild.

Independent transmission shops will usually repair what is needed while dealerships will usually just install a remanufactured transmission. The dealer's repair will get the car done faster with factory parts, and the new transmission will have any updated parts. Repairing just what is needed will cost less unless there are new and improved parts they want to install to increase reliability. Those are generalizations, but the place to start is with a diagnosis of the cause of the problem.