It doesn't have to be that way. I was also in Rome about six weeks ago. I booked a private guide through Context Tours, which limits each tour group to six people and provide guides with advanced degrees in the subject matter for an academic-like experience. My tour was at 8:00 and included the Sistine Chapel, Vatican Museum, and St. Peters Basilica. When the doors to the Vatican Museum opened at 8:00 am, our guide led us directly to the Sistine Chapel. There was maybe 50 people -- tops -- in the Chapel, including our group, and we were able to sit on the wooden benches, where the Cardinals used to sit, as the guide gave us a "college" lecture that lasted about 35 minutes. When we walked through the Sistine Chapel again about two hours later to get to another part of the museum, the place was packed like a NYC subway at rush hour.
I will follow your advice. Did you by any chance take one of the archeological tours beneath St. Peters? The crypt level is open, but I understand that one can tour the diggings deeper down, where one gets into the old Roman tombs.