Hi!
I’m about to build what you want from this power bank:
As I found out, it cannot be charged and used as a power supply at the same time. Applying input power switches out the output power. So I bought a cheap adjustable step-down (buck) regulator from ebay, adjusted to 4.20V, which fits into the leftover room over the PCB. I also fitted an additional 5.5mm DC input jack. Whenever 5V or more are present here, the regulator will charge with around 11W. As it needs around 17mA without input power, I will use an ideal diode from ebay (still in transit) between it and the batteries to prevent them from slowly discharging.
This way, I can recharge at any voltage (5-30V), and have 12V output at the same time.
If you are interested, I can upload images when I’m finished.