Latching control via active-high battery supply / regulator shutdown pin?
Using the shutdown pin you would need to add some diodes and a MOSFET to do what you want. However, as you have already guessed, the pull-down in the LDO adds to your quiescent current when it is off.







simulate this circuit &ndash; Schematic created using CircuitLab

A better solution would be to add in a P-MOSFET and shut off the regulator entirely. 







simulate this circuit

How that ties into the charging part though I am not sure.