Just a quick update on the car:
I had it towed to Darcars Chrysler of Fairfax on Tuesday afternoon, they looked at it early on Wednesday and told me that the problem was a pair of bad Transmission Speed Input/Output Sensors. The bizarre “low gear, no speedometer” symptom was the transmission’s failsafe mode that it goes into when it gets bad or irregular data from the sensors.
So they replaced the sensors and had the car ready for pickup by noon yesterday. They even gave me a break on the price ($15 off on labor, bringing it down to $197) since I’d had it in for this before. As far as I can tell in my travels yesterday and this morning, the problem is solved!