I missed your rabbit hole diving, but the batteries ownership issue would be handled between those few airports where these short but frequent trips would utilize this planes. Not a huge issue imo.
About the electrical interface, simply bolting down the batteries to the frames and having cables doing the connection seems like a reasonable approach.
You could even eject the whole battery frame in case of an oopsie.
Maybe I'm overlooking some important details here, but those 2 look entirely doable.
