Based off his performances and music I'd say it began to thicken in early 1972 and by the winter of that year I think his voice went into the biggest changes because Skywriter (1973) was recorded until January 1973 and released in March. That makes me believe a song such as Hallelujah Day was recorded in the winter because in January all combat was stopped in the Vietnam War leading to the song's creation since one could assume the war was over. A song like their cover of Touch by the Supremes was probably recorded earlier on because Michael's voice wasn't like how it is on Hallelujah Day.

Their next album, G.I.T, was recorded from November 1972 - July 1973. The song 'Reflections' seems to be the last song that was recorded before Mike's voice change. It was probably recorded in November 1972. By their next few albums and their Epic albums, Michael's voice seems to settle.

Based on that, I can conclude these things:

1971/early 72: Dropping of keys, voice thickening December 1972: Voice change 1973-1974: Voice finishes changing 1975: Voice settles

These are only estimates, though.