Jenny, I do not understand what you mean by your statement that if you buybthe "combined tour" from City Wonders they do not allow us time to tour the museum. You say they run you straight down the hall to the Sistine chapel and then send you off tomthe Basilica without seeing the Museum.
That is not how they describe the tour, nor was it our experience. We booked the Express Sistine Chapel and Vatican Museum with Dark Rome, which is a City Wonders "brand". As far as I know it is the same tour you are talking about, the one that enters the Vatican Muweum at 7:30 am. This:
https://darkrome.com/vatican-tours/sistine-chapel-early-access
They (City Wonders/Dark Rome) are indeed the first group allowed into the Sistine Chapel. You meet the tour at 7:20 on the steps and go through the Museum entrance at 7:30. I cannot speak to how fast they run you down the hall, because we were 3 minutes late to the meeting point and they already left. (It was Papal Audience Wednesday, and it took us much longer to get through the crowds in the plaza and around to the entrance than we had clocked the previous day). We found the Dark Rome coordinator and showed our tickets, and she said she would put us onnthe next available tour for entry. Which she did, putting us in the 8:00 group but with the caveat that we could not stay with them through the Museum because it was the guided tour which we did not pay for. That was fine with us, as we wanted to head tomthe Sistine Chapel first.
It was a long walk and we slowed a bit through the Map Room to admire the maps. When we got to the Sistine Chapel entrance we were admitted right away and found only about 20 other people there---presumably the group we missed, plus guides. We had the Chapel practically to ourselves for the next 10-15 minutes, before a few more people began dribbling in, and after another 10 minutes another group or two arrived ( by then the original group was leaving). We exited through the main exit into the museum and then were free to explore on our own, with no time limit.
I highly recommend that "Express" Tour if you want to experience the Sistine Chapel,in peace and quiet, without crowds. Just don't be late!