One plug disconnecting the other would certainly be nice. But interrupting the ground connection is a bit risky. If it's just a battery pack that's OK, but anything else (external power supply, "wall wart", ...) might have a different ground connection somewhere (ground loop), so trying to interrupt the ground pin would not work and give weird results.
Actually, the Axoloti seems to be prepared for X2 to disconnect plus from CN1: there is a trace from CN1 to the middle (plus) pin of X2, and then another trace from the outside plus pin of X2 to the rest of the circuit (R3, R4, D2, ...). Both plus pins of X2 are only connected on the backside of the PCB. So if you scratch through the trace there, you could connect one of those switching sockets to X2 (if it switches plus and not ground) and have the plug in your new socket take precedence over CN1.