My answer doesn't exactly answer your original question, but I have taken the Scavi tour (which was wonderful). Just as an FYI, the Scavi tour ends directly in St. Peter's Basilica. In other words, you bypass the sometimes lengthy line to get into St. Peter's. I highly suggest that you take this opportunity to explore the basilica.
What worked for me and my husband was to take the 9:15 Scavi tour, then we toured the basilica until about 12:30. When we left the basilica, we discovered the line for the museum was vastly shorter than in the morning (other RS posters have also noticed this). We only had a 20 minute wait to get in, then had the rest of the afternoon to tour the museum.
Our trip was in October of last year, as a frame of reference. I don't know if lines/timing/museum hours would be different for March. In any case, I hope you have a fabulous time.