Well... after a couple more weeks my 6-AA batteries still proved to be insufficient to keep powering the ESP32 (or at least enough to power up the WiFi). It's been chilly here, but barely below freezing at night, so temperature clearly isn't the culprit this time (or at least not the main one). Considering that it's in deep-sleep all the time, except for about 30 seconds every day, it seems that my power calculations were WAY off. My best guess is that the voltage regulator on the development board burns a LOT of power (well, lots is relative depending on your power source), and hence the order of magnitude less battery time I'm seeing. Fortunately, it dawned on me a few weeks ago that my mailbox is on an exterior wall that happens be be directly behind my washer/dryer AND there also happens to be a free outlet right there as well. It feels quite silly to say, but I just got done drilling a small hole through the exterior of my house so I could run a USB cable into my mailbox (and yes, I caulked it on both sides).
Not quite as satisfying as getting it all running on batteries, but now I won't ever have to deal with them either. Win some, lose some.