Ok Fantastic. Yes, the power supply can tolerate backfeed, but I might as well add a protection diode(D1). The batteries don't need to charge quickly, in fact, I would prefer them to charge slowly to avoid pulling too much current from the load. Does this diagram make sense?
Also, I think that BMS can be used in any configuration from 3S-7S. Correct me if I'm wrong, but to use 6S I would just short out the 7S lead to the 6S right?
Thanks!!