All jokes aside now - Dave did you set your upper part to either both, or EXT in driving the Harmony M?
I never had any issues with one when I had my Korgs - it worked fine. I used it for the same reason as you.. I was doing a similar thing in using audio in from a laptop and then an iPad.
Also ensure the Harm M has had the firmware upgrade - it does a few things, not the least of which is the chord recognition time is reduced by around 60%. Although it IS a complicated procedure so not many do it.
I kept my Harm M as it frees up totally what keyboard/software I want to use. No relying on the keyboard harmoniser.
Dennis