I was able to disassemble the car dock. It was all removable connectors (screws, etc.) except for one sticker that covered some screws, one rubber ring attached just above the suction cup, which obscured some screws, and the wire attached to the tiny PCB that held the microUSB port was soldered directly on. Oh, and standard plastic retention clips you see in everything. I had a spudger that made the disassembly of that much easier.

I was able to remove the stalk and suction-cup mount completely. Now I just have to figure out how to fabricate a more basic mount, and probably construct a small 12V to 5V DC/DC regulator circuit.