The Book Switch Theory

[ReneZ]

still I think could better explain some details that the SPT struggles to explain.

I guess 'SPT' is an abbreviation referring to the 'normal' storyline, i.e. no fake items and no fake signatures.

To be honest I am quite unsure which details it struggles to explain.

Some time before 1911, Wilfrid learns that the Jesuits have a secret stash of books in Rome that includes several volumes of Kircher's correspondence and many books that once were at the Collegio Romano, including books formerly in Kircher's library.

So far so good. We even know that he learned this from Joseph Strickland, probably when Strickland was still based in Florence. Except: the Kircher correspondence was not part of this discussion. There were two strictly separated collections, and the books that Voynich and the Vatican acquired together (230-ish in total) were in the smaller one.
But first let's go to your second point:

Wilfrid learns that, in that stash, there is a letter saying that Marci sent to Kircher a Bacon original.

Does this refer to the Marci letter, and do you mean that this used to be part of the Carteggio?
Because it never did. These letters are all listed in the indices, and they all have a stamped page number. No Marci letter from 1665 is missing from the index and the Marci letter has no stamped number.
Note that the earlier letter to Kircher from Moretus+Barschius is missing, and is also not lacking from the indices. It was never filed in the carteggio, even though Kircher responded to it, and perhaps it was kept in the Voynich MS as well. But we don't know and it does not matter.
 
Now back to the story.
To understand this situation better, it would beneficial to be able to read the book: "Danieluk S.J., Robert: La Bibliotheque de Carlos Sommervogel: le sommet de l'oeuvre bibliographique de la compagnie de Jesus (1890-1932), 2006.". This tells about the struggles of the official Jesuit bibliographer to update the complete bibliography of all Jesuit works, right during the time when much material is in hiding (1880's and 1890's). It is based on correspondence from this period preserved in Jesuit archives. He exhanged letters with several Jesuits in and near Rome.
In the end, his work, completed before 1911, does not include the Kircher carteggio, even though it includes lesser collections of material. He was not aware of its existence. This is how thoroughly this was hidden.

It would also help to read about the struggles of Hungarian historians who had seen photos of two manuscripts from Matthias Corvinus' library that were photographed in Rome before they were hidden. They were desperate to find these again and undertook several trips to Rome in search for them, in vain. The Jesuits must have been aware of this, because these two were among the first that were sold - for a fortune. These (and a few others) were much more valuable than the weird Voynich MS.

It may be tempting or even natural to think of the Voynich MS as the prize of this collection, but it really was not.

It may also be tempting to only think of the Kircher carteggio when it comes to the rest of the hidden collection, but these were only 12 or 14 volumes out of over 2000. I attach a photo of some shelves in the historical archives. Copyright of the photo is with APUG.

   

Just guessing, these could be some 400-500 books, so about twice the number the Vatican (together with Voynich) got. The other collection including the Kircher carteggio would be five times this lot. 

The significance of any individual letter in the Kircher carteggio is zero in this context. In any case, the collection was primarily known for its letters from Popes, emperors and missionaries across the globe. Not some obscure guys in Bohemia.