The Vatican itself offers and early-entry option that is considerably
less expensive than the early-morning commercial tours.
Right. The Vatican's options do involve breakfast at the museums. Here is the more affordable of their two options (€ 52,00 per adult) which goes directly to the Sistine upon beginning of the tour. It's 2 hours in length, breakfast excluded:
https://tickets.museivaticani.va/home/fromtag/5/1639461600000/VG-Musei
(It's the second one on the list; "Prime Experience - Vatican Museums."; group size of up to 15 )
Even with an early-entrance tour, you won't be alone in the Sistine 'cuz the Vatican plus any number of outside companies offer these. However, visitor numbers in the chapel will still be lighter than during general-public hours, and will probably be even lighter in December than during high season. It'll be interested to see when they open up the interior passage between Sistine and St. Peter's again? That passage is reserved for tours, and saves both shoe leather and time when those tours which include both museums + basilica are able to use it. If I knew that was going to happen with the next change of procedures, should that be soon, I'd suggest jumping on that option but it's anyone's best guess when that might be. 🧐