the H6 has excellent pre-amps, thus is not the bottleneckI'd like to understand why its a bad idea. Why won't the camera use the external sound signal as is?
capturing sound with H6 to your phone through a digital connection, and then replaying it over your Bose should sound close to the same as directly from your accordion
but I suppose you are connecting with an analog line
how exactly are you connecting it to the phone?