Aren't room induced discrepancies non minimum phase by nature, as they are a convolution of the original signal by a non minimum phase reflection pattern?
There's a discussion of this in Dr Toole's book. I can't link to that here, but there is some discussion of it in this
older article by Dr Toole, where he says:
"Room resonances at low frequencies behave as “minimum phase” phenomena, and so, if the amplitude vs. frequency characteristic is corrected, so also will the phase vs. frequency characteristic."
I think that is a slight over-simplification, but it is true in the case of at least some room modal behaviour.
There's also a discussion in John Mulcahy's
article on the REW website, where he says:
"Room responses are mixed phase, meaning there are some minimum phase regions and some regions that are not minimum phase. The minimum phase regions tend to be at lower frequencies, but we cannot simply say a response is minimum phase below some specific cutoff."
I know that's not a complete response to your question, but suffice it to say that room modal behaviour tends to be minimum phase, but the specific characteristics need to be measured in a given room to determine what behaviour is minimum phase and what is not.