Hi, Phil. There was another advantage to the way that you overdubbed your voice. Not specifically because of the MS, but important. You used the identical gain for each overdub. As a result, the same perspective of the stereo miking integrates them all.
Reminds me of when I recorded Stravinsky’s L’Histoire Du Soldat in two parts and mixed them later in post. Part one was the instruments and part two the narration and the acting. I insisted to the producer that we keep the same Blumlein pair mike up (An AKG C24) for the narration, at the identical gain used for the instruments. I positioned the actors in front of the mike at positions that sounded good — in the same hall. As a result, everything just flowed together in post. What happens if you decide to record the narration/acting at a different time, is you get a discontinuity, the ambience and the perspective changes. But instead, we got a continuous presentation that makes it sound precisely like the actors are there on stage with the musicians.