UPDATE: We made it home to Austin, TX
Back story: Birmingham supercharger went down on last day of trip, and the car had a lowish state of charge.
Front story: Tesla was able to Uber me back to my cousin's house while we left the vehicle hooked up to see if the Tesla SC would go ahead and charge the car just enough by morning (at an average 2mph, it didn't). The next day my cousin took us back to the SC and we called Tesla again to form up a plan. It turns out we had just enough charge to get to the Indigo hotel in Tuscaloosa, which was gracious enough to allow us to charge for free and even provided a free breakfast (slow waitstaff service related, not plight related). The moment we finished charging at Indigo (down to the second), the rain picked up and blew a transformer which knocked out power to the Hotel. Alabama was just trying to get rid of us by then
So after 3 hours of charging we were on our way to Meridian. The delay resulted in us staying the night at Shreveport, but everything generally worked out. We had no other SC drama the whole way back.
Root cause: According to Tesla, the Birmingham charger is down because of a grid issue. I'm told they are working on it with Alabama power, but do not have an ETA on when the charger will be back up. My money is on a voltage quality issue brought on by the rain that Alabama hasn't seen since the SC was installed.
Afterword/Shoutout: I was also able to message a few people on plugshare who had Tesla adapters at their homes, and a few of them responded with kind messages and offers for us to use their home chargers. Unfortunately, by that time we had already come up with a plan and were on our way. I really appreciate the plugshare community though and all those who responded to my pleas for help