Wish I had a recommendation but I do want to caution you to look at the tours offered by Viator and Get your Guide very carefully as neither actually conduct their own tours. They're 3rd-party consolidators of companies which do, and so you have to dig into the information to find out out who is actually leading the tour, and then search for reviews on that particular company. Booking directly through the actual company can also save $.
I'm also seeing some tours that advertise "Holy Doors" but if you read the info, it's unclear if they actually pass their clients through them (prior registration is required to do that). For instance, this one?
https://www.viator.com/tours/Rome/3-Major-Vatican-Basilicas-outside-the-Vatican-Small-Group-Tour/d511-62570P47?m=63845&supag=&supca=20927319006&supsc=&supai=&supap=&supdv=c&supnt=nt:x&suplp=9019649&supli=&supti=&tsem=true&supci=&supap1=&supap2=&gad_source=1&gbraid=0AAAAAD-gbd5_7_eR0I3MRcX6kMS2nHMVF&gclid=EAIaIQobChMImvHu0YjwigMV611_AB04HDJeEAAYAiAAEgLKEfD_BwE
The description says that the group will "see the Holy Doors", not that they'll be passing through them such as a pilgrimage journey involves. There are only 11 reviews for this tour, and ALL of them are dated before the doors were opened for Jubilee. Hidden under "Additional information" is the operator: E & D Guided Tours. Further searching turns up that company as "More Of Rome": E&D probably stands for Emanuela and Dimitri, their founder and booking managers.
It is essentially this tour on More Of Rome/E &D's own website, and what it's priced at on Viator - from $125.29 per adult - is priced at 80,00€ (roughly $82.00 today) on their own site.
https://www.moreofrome.com/tours/vatican-basilicas/
Get Your Guide prices it at "from $117.87" and hides the operator (E&D) even deeper. This tour is not available for weekends or Friday PMs so wouldn't work for you but it's a good example of booking any tour through a consolidator carefully, OK?
