There's audio of a discussion between Br. Peter and someone discussing the te igitur, which is worth listening to. The basic premise is that this prayer is supposed to show unity with the chair of Peter, not the man occupying it, which is accidental.

Let me ask, in the Canon's unity with the Seat prayer, why does the celebrant have to say the name of the heretic?

He is in union with the Seat of Peter, not the pachamama worshiping anti-pope.

As I was a parishioner at this chapel from 2009-early 2012 (the time period in which the transition from independent to SSPX commenced), I’m in a position to nuance these comments a bit:

The resident priest (Fr. O’Connor) was preparing to retire, and the board was quite naturally actively seeking his replacement/successor.

The SSPX was invited by the board to consider sending a priest, and through then-District Superior Fr. Rostand, at a public meeting to which all the faithful were invited to attend (and which I in fact did attend), Fr. Rostand made a presentation and fielded questions from the faithful.

During the Q/A session, I asked whether  we would ever see Bishop Williamson back in active ministry again (ie., this was at the time when he had been sequestered to the Wimbledon attic), as a few of us were newly concerned about what this sequestration might imply for the future direction the SSPX might take.

At a certain point in the Q/A session, Fr. Rostand declared (paraphrasing from memory) something to the effect that, “If our help is not wanted, I can take my priests and go.  There are plenty of other places looking for priests.” In other words, he did not give the impression of a corporate raider eager for a takeover of a rival.

Anyway, the standard practice was to agree to a one-year probationary period, for each side to get to know the other, before coming to a final board vote.

One if the conditions is that ownership of the property is transferred to the SSPX.  Absolutely, with 20-20 hindsight, one could say that had the process commenced post-2012, some would not have supported the board approval (or perhaps even the board itself would not have approved), but the point here is that whatever may or may not have transpired with independent Chapels being turned over to the SSPX elsewhere, this one happened with the overwhelming support of most of the chapel, and so far as I am aware, most of them have been happy with the results.

Had this all happened in 2013, maybe they would have invited a Resistance priest instead (but even in that case, they would still have wanted ownership of the chapel as a condition for accepting, in order that the faithful not exercise an impertinent leverage over the priest).  I am aware some independent priest who sympathize with the Resistance might not have that precondition, but they put themselves in a precarious position.

As for the assertion that Fr. Rostand threatened to set up shop down the road if ownership was not surrendered, I can’t disprove the veracity of that claim, but it would seem incongruous with the ready willingness to take his priests elsewhere which he exhibited at the Q/A session I attended.

Here we are in 2013, with the SSPX at independent chapel in downtown Santa Clara, CA
(This property is worth $2 million).

I will never buy the idea that Fr. Rostand was not salivating over the idea of nabbing a turn-key chapel worth $1million.

Just playing devil's advocate here:  Was St. Vincent Ferrer offering Mass while naming an apostate who worshipped pagan idols in his Church?

While I do agree that the Bishop Dolan is wrong on the "una cuм" issue, I don't think this example is equivalent to the current situation.

It doesn't matter because Benedict was not the Pope, it, by +Dolan and co.'s theory, would still constitute sacrilege.

If things are unclear and the intent is to pray for the Holy Father then there is no schism.  The intent of schism must be present for there to be sin.  No Trad has/can prove sedevacantism 100% so the "una cuм" controversy is an uncharitable, divisive, colossal nothing burger.