Unfortunately, the other thread didn't answer the question either!
It in fact muddies the waters further, implying that there exist "always on" USB power banks, but not citing any such devices (and "always on" is too generic to get useful results, in my brief googling just now). The OP is asking for specific suggestions, and looking at some of the other things he's considering, he's pretty desperate.
The other question, probably even more useful, is whether there is a generic way to lobotomize a power bank such that it doesn't do that anymore. How do they detect the current? Probably with a shunt, I mean, how else...? That suggests that one should be able to find that shunt, cut the sense trace, and then use a voltage divider to get an appropriate voltage on the sense pin so it thinks it's under an appropriate voltage.