(I know this question has been languishing for a while, but I only just noticed it. I figured I may as well chime in.)
The phase reversal feature on the MIC2200 basically flips your audio waveform upside down. It's sometimes used for noise cancellation in pure audio applications (audio engineers sometimes set up a second mic near a noise source and set it to the opposite phase of the main mic so that the signal from the "noise mic" cancels out the noise picked up from the main mic.)
However it shouldn't make much of a difference if you're operating in single sideband mode (USB/LSB). Your output RF envelope should look much the same regardless of how it's set, and at least for me, I don't notice much change in the way I sound when listening in the monitor on my TS-950SDX.
On AM mode, it has the effect of swapping your positive and negative peaks, which may be useful if your voice has some asymmetry in it (which most voices do -- mine does). Asymmetry means that you may have higher peaks in one direction compared to the other. You see this in complex audio waveforms like speech, as opposed to a simple waveform like a whistle (which is just a pure sine wave).
Ideally, when operating in AM mode, you'd like those higher peaks to correspond to your positive peaks, since that means you may get more positive modulation without your negative peaks going completely to zero. If you examine your RF envelope on a scope and you see that things are the opposite (i.e. your negative peaks are more pronounced than the positive), you can hit the phase reverse switch to swap things around.
When I do this on AM, at least with my rig and my voice, the resulting oscilloscope display shows higher positive peaks than negative and the audio sounds clearer (I think this is because with the phase the wrong way, the excessive negative peaks cause overmodulation in the negative direction which results in distortion, but I could be wrong).
If you're operating in SSB though, I can't account for the apparent difference in how your audio sounds, because it shouldn't change that much. However, it's possible that the way the MIC2200 works, they're feeding the audio through a separate buffer stage in order to achieve the phase reversal, and maybe that buffer amplifier is changing the characteristics of the audio waveform somehow, aside from just flipping the phase (which really it shouldn't do).
Note that I think Mike WZ5Q is in the middle of moving to a new QTH so it might be a while before he throws his two cents in.
-Bill, N1GPT