TPU cases don't work
I picked up a "TPU" case via eBay (pic attached). It's similar to the silicone skins except the material is a little stiffer and has a glossy finish (which I prefer).
Without the insert, the phone does fit physically in the dock, but the contact with the dock connector is poor. I may need to do what h8zgray wrote and that is to put some kind of pad on the right side of the dock to help hold up the phone. I think I have some left over weatherstripping I could use...
For the time being, I'm using an Arkon Mega Grip mount in my car.
I found it ironic that the dock doesn't work with some of the "official" Sprint cases, like the gray plastic two-piece case.
I hope someone can find a good case that will fit.
Update: Another member posted a comment in another thread that enlarging the notch surrounding the USB/microHDMI port could help make cases fit the car dock. There's a raised area in the dock surrounding the USB connector. I took a second TPU case and enlarged the opening for the USB/microHDMI ports and that made the case work in the dock. The connection is a little loose but I think adding a thin strip of padding to the right side of the dock might help keep the phone and case stable. So the stock TPU case won't work without this modification.