I received a call back from the customer service/care people who confirmed that this is a known issue but that there was a workaround until there was a software update to fix it. I tried the workaround - which is plugging in the car, turning off, then turning back on the charging schedule. Of course, this workaround did not work for us.
I also took it to the dealer who was able to replicate that there was something amiss - initially they set the schedule to 1pm and it started charging. But then they reset the schedule to 3pm and plugged in the car. When the service person went back to check it at 3pm, the car was at 100% so he knew that the car continued to charge even though the schedule was set to start at 3pm. They placed a call into "engineering" but said there was nothing more for them to do. I called customer service/care people later that afternoon and have yet to hear back. I also called my salesperson (different dealership than where I'm taking the car to be serviced). He said he would make some calls and find out what he could about the issue, specifically whether there was an ETA to get a fix out there. I'll report back when I find out more.
Until then, our plan is to manually charge the car - plugging in as normal when we get home, and then using the UConnect app to "charge now" every night at 11pm. Or get Chrysler to somehow pay for a Level 2 charger with its own scheduler.