Well, a few days ago, I opened up the clock app so that I could observe seconds and not just minutes. The clock would tick forward normally for a while, and then at the top of a new minute, it might jump back by anywhere from several seconds to a full minute. Then it would advance forward for a while, and then suddenly jump forward by 1 or 2 minutes. Overall it was staying in the ballpark of the correct time, but it was repeatedly jumping backward and forward by anywhere from several seconds to 2 minutes.
I suspected that this strange clock behavior was causing the battery drain, so I disabled Use Network-Provided Time, and the battery has been fine ever since.
What I think might have been happening is that the phone was getting network time from two different sources, perhaps with a lag on one of them causing them to disagree by a significant amount. I live in a low signal area, and have a network extender that connects to the modem to communicate over the internet and provide a cell signal throughout the house and immediate surroundings. Not sure what would have suddenly changed, but maybe the neighbors across the street switched from AT&T to Verizon and swapped out their own equipment so that I was getting a second Verizon signal from them. Either that or maybe the Verizon signal itself has improved enough to start getting at least a partial signal without the extender.
Anyway, with Use Network-Provided Time disabled, the phone is happy.