I, too, voted for MTM as the most underrated album. While this is still my least favorite album in LP's discography, I really do appreciate what the band was trying to accomplish by going in an almost entirely new direction with their sound. My main reason for not liking MTM as much as the other albums is that I feel it really struggles to find an identity. The first half of the album has a decent mix of light and heavy songs but then becomes increasingly soft in the last quarter, starting from Valentine's Day onwards. I just personally feel that there were too many "softer" songs and not enough heavier, more energetic songs. Overall, MTM had a solid concept by trying to make every song distinct but ultimately could not find a consistent theme and wavered too often. Lastly, when I say "softer," I mean songs that lacked the harsh, aggressive vocals and intense instrumentation that the band was known for at that point, before they entered their grand phase of experimentation.
To speak on your point about Minutes not having an identity because of the unorthodox order of songs, I recall Mike saying in an interview that this was done purposely. He said something along the lines of trying to put a focus on the differences in sound from song to song. It was probably done to strengthen the shock factor of the album.