Cautious optimism that I may have solved my problem. Here's what seems to have worked (I say seems because a couple times today I have had spikes where the phone gets warm and Home & Lock Screen use over 40% of the battery, but it eventually calms down--maybe just reindexing my 150 gigs of phone data.)
This time I took the phone into recovery mode while connected to the computer (If you can't update or restore your iPhone or iPod touch - Apple Support) and restored the software, which wipes the phone and reinstalls the system software from scratch. After this was done I restored from my last iCloud backup. I did this because I have over 100 apps on the phone, and really didn't relish resetting up my entire home screen, and re-inputting every.single.password. After that, I let it index overnight.
When I got up this morning I started working on the phone and after 10 minutes the battery still hadn't dropped even 1%, a dramatic improvement. However midway through the day I saw that suddenly the battery was dropping and the phone was getting warm again, so I turned on reduced energy mode and use the phone for a little while, then I turned off reduced energy mode and the battery seems to be holding pretty well. I'll follow up again after I know for sure.--Home & Lock Screen was using 46% of batteryWhen I got up this morning I started working on the phone and after 10 minutes the battery still hadn't dropped even one percent, I dramatic improvement. However, midway through the day, I saw that suddenly the battery was dropping and the phone was getting quite warm again (Home & Lock Screen again), so I turned on reduce energy mode and use the phone for a little while, then I turned off reduce energy mode in the battery seems to be holding pretty well. I'll follow up again after I know for sure.
Crazy process, and crazy that Apple expects the average user to go through these steps to fix *their* problem.