There are many approaches to live sound and it may take me a while but, I plan on sharing my experiences with setups and playing the keyboard harmonica in a live setting.
One quick experiment that may not be too costly (about $75 dollars) is to try a suction cup or contact microphone. I have yet to try one, but just discovered the website below that sells high quality, medical-grade contact microphones. They also sell suction cup microphones with a piezo microphone in the middle of the suction cup. This arrangement could attenuate ambient noise while still providing a natural sound. I don’t know. I have not tried them yet but the concept seems like it should work and that is what the website claims.
The contact microphone website is: http://www.contactmicrophones.com/
You know a contact or suction cup microphone might actually enhance the sound of the melodica for some genres, and the bleed through would not be distorted. Or the contact or suction cup microphone could work lousy and sound like crap.
If someone does an experiment, let us know. Just ensure the contact microphone website has a good return policy.