I use power banks that are shells for 18650 batteries. The brand name is Tomo. My Aftershokz are OpenComm and I also have wired Sportz Titanium. They draw around 100mA when charged, 80mA for OpenComm and 125mA for Sportz. Those banks seem to charge them without shutting down.
Do you like the Tomo P2 or another one?