The only problem with most such, and probably Rick's too, is they start at the beginning and take you through the one way system, showing you things along the way, all the way until you get to the Sistine Chapel which is at the very far end of the somewhat linear Vatican Museums.
What you want to do is start at the end and work backwards towards the entry. That may be difficult with audio tours, or at least take plenty more work. I'd advise downloading and checking carefully if anything will work in the way you want to use it.
By booking two very major events (not cheap either) so close together I hope you aren't setting yourself up for timing difficulties. My understanding of the Scavi tour is that they don't wait for you.