How to extend Paperwhite battery life with a powerbank

[handyguy]

Hi,
I have hacked my PW to be a standalone clock. With the internal battery, I get about 1 week of life before recharging is needed. I thought I could add attach a small battery pack behind the PW (no AC outlet is nearby) and get much more time before recharging is needed. However, with my 20,000mah (14x the internal battery capacity) I am only getting 2x (2 weeks) the duration.
I think this is because of the oddity of the PW current draw at or near 100% of a fully charged PW.
Any ideas on timings for a circuit I might use between the PW and the power-bank that could 'game' the system, i.e. keep the PW from pulling un-necessary current.