Hey there frinet,
As far as I know identical overlays do not have unique IDs to them. You’d normally need to reprogram the Morph each time to change the functionality.
or if you can program the desired configuration into the “No Overlay” mode, then it might be possible to have one of your two overlays look like “No Overlay” to the Morph. That way one Piano overlay would be the normal functionality, and the other would trigger the “No Overlay” custom configuration.
This is just speculation since I haven’t worked that much with customizing overlays.