A "correct" interpretation depends in large part on one's assumptions (or presuppositions). A covenant theologian might presuppose the Church (i.e., the "holy Catholic--or universal--and apostolic church" began in Abraham's tent, whereas a theologian of a different stripe might presuppose the Church was yet future, as Christ seems to indicate in Matthew 16:18, where we read
"'And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.'"
Rather than "taking sides" on this issue (which is really quite controversial and tends to generate some pretty "intense fellowship" among well meaning Christians), I'll say in my typically wishy-washy way: Both sides are "correct"! In a sense, the Church was started in Abe's tent; likewise, in a sense, the Church was yet future when Christ commended Peter for his declaration
"Thou art the Christ, the Son of the living God" (Matthew 16:16; Mark 8:29).
I also agree with John Piper, whom you quote as follows:
"The mystery is this: God did not create the union of Christ and the church after the pattern of human marriage; just the reverse! He created human marriage on the pattern of Christ's relation to the church."
I would even go a step further by saying, the pattern for Christ and the Church originated in the eternal counsels of the Triune God--Father, Son, and Holy Spirit. I hope I will never tire in saying that the very notion of love, agape love, is rooted in the tripartite nature of the Triune God. How else could the Apostle John say in His first letter,
"God is love" (4:8 and 16)?
Biblical love, not the often lustful and hedonistic love of the human-like gods in the Greek and Roman pantheons of gods, but the deliberately self-sacrificing love of a God who is love, is inherent in the very nature of relationship, whether to an infinite degree in the Godhead or to a lesser degree in human relationships, particular the relationship between a husband and wife.
With a firm understanding from a biblical perspective on the very nature of love, we can then move on to at least a partial understanding of the mystery whereof Paul speaks in
Regardless of your presuppositions (to which I referred, above), the notion of a Church Universal is not an Old Testament concept, by any stretch of the imagination. There are hints here and there, of course, regarding what God would one day do in calling out a people for Himself from among not only Jesus' own people, who largely rejected Him as the "King of the Jews" and as the Messiah when He came to earth (see John 1:11), but also from among the heathen nations, commonly referred to in Scripture as the "Gentiles" (globally) and "aliens," "sojourners," and "strangers" (locally). See, for example, this very brief overview of how God included the Gentiles in His redemptive plan throughout the OT era. Also, consider reading the following passages from the OT:
Genesis 14:3b (". . . all the families of the earth will be blessed")
Leviticus 25:35 (Israel was to welcome a poor sojourner into their midst)
Numbers 35:15 (sojourners who committed inadvertent manslaughter were free to flee to the cities of refuge)
Jonah (God sent a preacher to get the Ninevites to repent, and to Jonah's surprise, they did, even though he didn't want them to!)
Exodus 9:14 & 16 (where God chose Pharoah and Egypt through whom He would reveal His power to the world and so that His might would "be proclaimed in all the earth")
Isaiah 56:6-8 (where the prophet speaks of foreigners being brought to God's holy mountain, Jerusalem, where His temple is and where Jesus during His earthly ministry declared that temple to be a "house of prayer for all nations," Matthew 21:13 and Mark 11:17)
Jeremiah 1:5; 3:17 (where the prophet was appointed by God as a prophet to the nations, and where the prophet spoke of all nations being gathered to "Jerusalem, the throne of YHWH")
Ruth (where a Gentile became an ancestor of Christ!)
Judges 2:9,11 (where a prostitute identified with Israel and their God, and who--along with Ruth, later on--became part of Messiah's genealogy)
Despite the many hints in the Tanakh that God would one day extend His gracious offer of forgiveness to all, including the Gentiles, who would simply repent and believe in His Son, the very concept of a universal body of believers who were neither Jews according to the flesh, nor even schooled in--not to mention even aware of--Judaism as the religion through whom the one true God was revealed to the patriarchs (especially, Abraham, Isaac, and Jacob), was foreign to God's chosen people.
The Apostle Paul, from whose pen came the words "the mystery of Christ and the church," was before His conversion completely in the dark, spiritually, about both Jesus' identity and His mission of building His church, against which even the gates of Hell would not succeed in defeating.
In conclusion, perhaps the greatest aspect of the mystery of which Paul wrote, is the mystery of the grand sweep of history from God's perspective, which is documented, in part only, in the OT Scripture. The writer to the Hebrews said that the patriarchs and the many other people of faith, both within and without Judaism, some of whom, like Abraham, dwelt in tents,
". . . looked for [by faith] the city which has foundations, whose architect and builder is God" (Hebrews 11:9, 10).
The writer also said,
"All these [righteous saints] died in faith, without receiving the promises, but having seen them and having welcomed them from a distance, and having confessed that they were strangers and exiles on the earth. For those who say such things make it clear that they are seeking a country . . . a better country . . . a heavenly one . . . [and] God has prepared a city for them" (11:13-16, excerpts).
That grand sweep of history was presaged in the institution of holy matrimony, which God designed to be a covenant between one man and one woman who, in love, would pledge themselves one to the other in a relationship characterized by devotion, sacrifice, fidelity, and love in action--agape love, 'til death parts them.
In similar manner, God pledged to the patriarchs that through them all the families of the earth would one day be blessed by being drawn into, by God's grace, the forever-family of Jesus Christ, who is the Head of the body, which is His church (Ephesians 5:23 NIV, and Colossians 1:18 NIV).