Thank you for that suggestion. I tried holding and double pressing the button. A double press gets me the green light, and I think it does keep the PowerCore Slim 10000 on a little longer - maybe 1 hour instead of 30 minutes. But I need the USB battery pack to be on even longer.
I am powering a DSLR camera from the higher current USB-C output and I need it to be able to do that for several days if possible. Through a DC-to-DC USB output device on the USB-A output, I have a 1kohm resistor and LED. I estimate the power there to be about 0.1W, and that has kept the PowerCore Slim on for two days now. I might only have a few more hours left on the USB battery pack though.
Surely I could come up with sexier ways to keep the power output stable, but I thought I would share this option for anybody with the same challenge.