I finally cut up one of the micro USB cables, and tried a couple voltages on the USB charge input.

1.5V - no result.

3.27V - the charge lights lighted. 5V probably appeared on the bank's output, but I have to confirm that.

The next step will be to dig up an old solar patio light. I should be able to get at least 3V from the solar cell, and I'll see what happens with that.