I agree that a headset mic, at least on the quieter voice is the easiest way. So you only need one headset mic. Also, a headset mic which is unidirectional can be positioned to reject the louder voice.
Doing it this way you will probably have to turn the gain down on the quieter voice in relation to the louder one.
Yoy will have solved both problems: the phase cancellation issue and any increased room reverb from the high gain mic on the quiet voice.
