one Christ = one earthly hierarchy?

I am broadly in sympathy with Frame's goal, here; I agree with much that he says that could be summarized in Christ's statement, "It must needs be that divisions and offences come; but woe to him by whom they come!" I hope we can see more and more readiness to dissolve the old stumbling-blocks that keep Christ's people arguing with each other when they could be reaching the world.

And yet, I find myself uncomfortable with his case for a unified organization, insofar as it focuses on the organization as such rather than the organization as a by-product of confessional and goal-oriented unity. There are a few nits I'd have to pick before I could jump into the bandwagon, here.

For example, Frame says:

1. As in the Old Testament, the New Testament believer worships at a central altar, for Christ himself fulfills the central altar of the Old Testament, and there is only one Christ (Acts 4:12; 1 Cor. 1:13; 8:6; Eph. 4:4-6). The same is true for the priesthood, the temple, and the sacrifices. The church has a single location in one sense, though it is scattered throughout the earth, for it is seated with Christ in the heavenlies (Eph. 1:3,20; 2:6; 3:10; 6:12). [14]

Frame interprets this, I take it, as a basis for seeing the church in all places as one organization (which he then suggests is one organization sinfully fractured). And yet, I fail to see how "one Christ" or the eschatologically-oriented "seated with Christ in the heavenlies" (we are obviously not there, cf. 2 Cor 5) is like the central altar in precisely that respect Frame needs it to be: material, earthly organization.

Consider, for a moment, that Israel had One God, to whom they all looked from any place; and also one altar, to which they were to return for the rites related to body, blood, and atonement. Christians have one God in Christ, but we manifestly do not have one altar in that same sense. To have the equivalent of the central altar, God need only have instructed us to return periodically to some one place, where (for example) communion would be held. Yet Christ seems to have specifically pushed us away from any such notion of centralized worship:

Jesus said to her, "Woman, believe me, the hour is coming when neither on this mountain nor in Jerusalem will you worship the Father. You worship what you do not know; we worship what we know, for salvation is from the Jews. But the hour is coming, and is now here, when the true worshipers will worship the Father in spirit and truth, for the Father is seeking such people to worship him. God is spirit, and those who worship him must worship in spirit and truth."

(I'll split these into chunks to keep it manageable.) Do consider this passage in light of Frame's thesis, though. At the very least, ought our concern not be first for unity of spirit and unity of truth, or as I suggest confessional and goal-oriented unity, with organizational unity at most a hoped-for byproduct? (though it would be an inevitable byproduct, I think, just as divided organizations are the inevitable byproduct of striving "spirit" and distorted "truth")

[UPDATE: egregious misquoting of Scripture fixed. Sincere apologies for an honest and embarrassing misremembering of the text.]