On the occasion of this discussion, I looked around whether anything surfaced regarding the battery drain for Tomo power banks. As an alternative to Tomo, Xtar banks have been actually suggested as exhibiting far less drain and better efficiency. I got Xtar PBS2 and it charges Aftershokz fine. Incidentally the ability to charge Aftershokz in the field is important for me too - I just did not realize that there might be a potential problem there.
Xtar is bulkier than Tomo, in my opinion unnecessarily. Another advice online is to modify circuitry in Tomo to eliminate drain and to change diodes to increase its efficiency. However, my reliance on the Tomo units does not justify going this far. For the moment it will be Xtar for 2 cells and will be trying Qidian for 3 cells. My 8 cell bank was made by Qidian as I determined.