The Mozart “Ave Verum Corpus” led me to the Benedetti progression.    To Benedetti (16th century mathematician) I’d say: your progression is one of those a composer shouldn’t write.   Mozart shows us how to do it better.

In the above research, a much more interesting case might have resulted from an understanding of the music:  just as in Mozart, the supertonic can and should change pitch in response to ‘which side’ of the tonal universe it falls: subdominant or dominant.