GPS fix frozen across town

An hour ago, we were visiting friends across town. Now we're back home, and my Model X, Pensive, is plugged-in to the outlet in my garage; but it still thinks it's across town.

Full message submitted to Tesla:

New issues tonight, when visiting friends across town; looking for any input or suggestions for handling this either now or in the future if it resolves itself this time:

Upon arrival, the car initially would not indicate that we were in park (despite multiple tappings of the "P" button on the gear lever). Effectively, the car may have been in either park or with (H), or may have been on flat enough ground at the time; when I was about to check (either opening door or tapping the accelerator?) the car switched to park and displayed the door screen in the MCU. Since leaving, the car has not updated its location.

On the trip I restarted the MCU (two button hold on the steering wheel), and the car had indicated moderate LTE strength. Parked, it still has not updated its location inside of my garage. It would not open when I pressed the button on the mobile charger (120V). Accessing it via the app, it showed the location across town, but I was able to open the charger port, and upon inserting the plug, the car responded normally.

Since I'm still shuffling paper with home charging, Pensive still charges on 120V@15A at home. I did get a cursory response to my request yesterday, but not really any support.