It occurs to me that if one were to put a switch (SPDT) in the V+ to the on-board regulator, with common to the regulator's Vin, the on position connecting that common to V+, and the off position connecting Vin to GND, the runaway MCU might occur much less often during power-down.

Of course,this would require a protection diode across the regulator, conducting from the (regulated) Vcc capacitors to the (unregulated) Vin terminal.

RE