Update: The Jeep went to the dealer's this morning, and drove perfectly all the way there. The CEL went out a couple of days (and start/stop cycles) later. Within an hour, they told me there were a few software updates (transmission, BCM, etc.) due, along with the brake booster shield recall and annual inspection. Beyond that, they will be replacing the transmission valve body; apparently, the replacement part has been redesigned, as there have been a few failures noted lately.
I expect to hear from them tomorrow. In the meantime, I was loaned a 2013 Avenger (no, they did not have a spare Hellcat to loan out