I think the difference between us is mostly semantic, subtle differences in the meaning and use the terms, such as "institutional," but we should continue the dialogue as I think we both sharpen our understandings thereby.
The shepherd being struck, the sheep are "scattered." Zech. 13:7. This scattering can be witnessed today: those united in faith but separated, Sedes, Resistance, SSPX, etc. There is no organized structure; their union is not "institutional" or organizational, but by doctrine or faith.
These sheep were indeed formally part of an institution called the Catholic Church; they existed within the institution, with, as you say, "tares" among them in the kingdom. This is no longer the case. To the extent there are the elect within the NO, their election is no longer institutional in any sense, as the institution has been abandoned by the other elect sheep with whom they remain united in faith. Again, the union of the sheep now is doctrinal, in Christ by the Spirit, and not organizational or institutional, as they are disparate and scattered, and not united in a single organized institution, as formally.
If you want to call this union of the faithful the Catholic Church, and identify the Catholic Church with the "church of the firstborn," fine, but as you yourself concede, within that Catholic Church were individuals who were not Christ's Sheep, who were not in fact true members of the "church of the firstborn."
The fact that the institution is not coextensive with the "church of the firstborn" is now made clear by history and circuмstance. The institution was used indeed used by God for the spread of the Gospel and the gathering of the wheat; it was the external representation or figure of the "church of the firstborn," but the institution was NOT strictly speaking the "church of the firstborn."
We know this now because the "church of the firstborn" still exists on earth, members of it on this forum, discussing and sharing the faith of Christ, but not united in an organized body, an institution with spiritual authority over each of the members. Your "bishop" has no authority over me, even if we were in the same geographical location, even if we were next door to each other. I could worship God in a different Catholic Church in the same city as you, with a different organizational structure.
The Novus Ordites, however, are in an institution under a central, organized authority, the institution we all - or our families - were members of. That institution has defected.
The "true church" was found in the institution formerly, but no longer. Just as the elect were found in Jeruslam/Israel, but after Christ's advent and the "calling out" from that defected institution, it was no longer.
Again, I think we agree. This is just a different use and understanding of some of the tags or terms used to describe the current experience.
DR, you mentioned certain verses from Apocalypse 11 earlier. Consider these verses that are clearly talking about the "institution" of the Church:
1 And there was given me a reed like unto a rod: and it was said to me: Arise, and measure the temple of God, and the altar and them that adore therein.
Et datus est mihi calamus similis virgae, et dictum est mihi : Surge, et metire templum Dei, et altare, et adorantes in eo :
2 But the court, which is without the temple, cast out, and measure it not: because it is given unto the Gentiles, and the holy city they shall tread under foot two and forty months:
atrium autem, quod est foris templum, ejice foras, et ne metiaris illud : quoniam datum est gentibus, et civitatem sanctam calcabunt mensibus quadraginta duobus :
Notice how there is a split in this "Temple," or "Church":
1. INSIDE: There is the true "temple of God," where one will find "the altar" (not a meal table) and "them that adore therein." This is the true Church, not a building, but rather the faithful along with all that is necessary (priests, altar, etc) to adore therein.
2. OUTSIDE: There is the "the court." This is signifying what was known in the Jerusalem temple as the "court of the Gentiles." The gentiles were those spiritually "outside" of the Israelite religion. They were not allowed enter the temple proper because they would defile it. These are heretics, schismatics, etc. in our day. These are those who defile "the holy city" for "two and forty months." These are the followers of the Beast and the Ten Horns. This is the Novus Ordo, Neo-pagan, parallel, counterfeit Church, which is not really the Roman Catholic Church but situates itself in the same "place" ("the holy city") as the True Church, the "temple of God."
In other words, both groups appear to do something in the location of the Temple structure, figuratively. One group adores God and the other group (who are defilers and outsiders) "trample on" the true Temple, the true adoration, and the true God. Both groups exist together, at the same time. One group belongs in "the temple of God," the other group does not. This is describing the "revolt" or "apostasy" in 2 Thessalonians 2.
The description above uses the physical, historical, ancient temple in Jerusalem as a figure to hint at what is going on now, in the end times. It is not going to actually happen in a city called Jerusalem in Palestine. It is happening in the Roman Catholic Church/Faith, the New Jerusalem.
Also, it is the bad guys who are "outside." The good guys remain "inside." Why, because the Church is eternal. The true Faith does not change. In other words, the heretics (those following novelties) have left "the Church," not those who keep the Faith. The Church is where the Faith is (and the Sacraments and those who confect the Eucharist). As long as there are faithful Catholics with all the necessities for the adoration of God in "the temple of God," there will be a "Church." And this concept of "the Church" is the same "Church" that is described as "indefectible," following Our Lord's comment that the "gates of Hell will not prevail against it."
So, the Temple or Church (the place of sacrifice and adoration of God) is not describing permanent physical buildings and juridical offices necessarily. These things are historically accidental, not necessary. We know this because the early Church did not have those external things.
What is necessary is to have Jesus "in the temple." This happens when we have a true priest who confects the Most Blessed Sacrament during the Holy Sacrifice of the Mass at the altar. Jesus Christ is the Head of "the Church." He is with us, until the end of the age, in the Eucharist. All who are gathered (or desire to gather), in the true Faith, around His Real Body are in His Church until the end of time. The institutional, physical locations where this happens are manifestations of the institutional, physical Church. The bishops/priests who confect the Eucharist along with the laity who adore are the visible society that gathers in this "Church" with the true Faith in their hearts. Again, this is just as it was in the catacombs of the early Church. Nothing more is necessary to maintain "indefectibility."
I'm not sure exactly what you mean by "the Church of the First-born." If you mean the "first-fruits," then I think that group is a part of the faithful remnant, the best part. They are referred to as the 144,000 in the Apocalypse. They are the first to be "harvested" in the three "harvests" mentioned in the Apocalypse. Again, this "harvest" metaphor goes back to gathering up the wheat to be put into the barn.
I'll stop. Hopefully, I haven't confused things.