What hasn't been addressed and my point with a few commercial software being used is "excess phase" correction at low frequencies. I have tried MMM technique several times and it does not deal with excess phase at low frequencies. I have also tried MMM with rePhase for excess phase correction and is not the same, but closer, to the commercial software. What I am discussing isn't "magic."
In this article, one can see in the time domain a maximum phase peak caused by low frequency room reflections, that are corrected in the time domain. It certainly is audible to my ears.