While I wait for the battery to charge - I'm thinking about how to make it last a bit longer. To keep my end simple, I used a Adafruit PowerBoost board. This also allows low battery detection and shutoff ( Not yet wired or coded ). I can see the typical consumption runs about 50 milliamps without sleeping - but that doubles on a sample send.
1. Add sleep mode while awaiting a GET.
2. Add low-batt detection and shutdown.
3. Add charging circuit.