After my failures with the Adafruit Powerboost 1000 (post 16), I complained at an Adafruit forum. Their response as that I should have used a Powerboost 1000C instead. Note the subtly added letter "C". So, gritting my teeth, I paid $19.99 (plus their pricey shipping) and tried again.
I let this setup run for over 24 hours powering either a Raspberry Pi (drawing about .4 amps) or a Particle Photon (drawing 1/8th as much) and both worked fine. I could disconnect external USB without the computers noticing but pulling the battery plug caused both processors to restart. Not nice but not a deal killer.
Note the input power LED in the image. If you aimed a photo sensor at it, your program could detect external power failure. You would then have time to send out a text message and shut down "gracefully" whatever that means.
Update: The setup ran a Raspberry Pi for over 2 weeks.