The Source of Our DNA
Starting with your analogy of the DNA of Christ, I suggest that all the gifts reside in Christ to perfection.
Jesus was the apostle from heaven who was sent by his Father to save the world from sin. In the words of Isaiah, the Son said to the Father, "Here am I. Send me" (6:8).
Jesus was the epitome of the prophet, in who are hidden all the treasures of both wisdom and knowledge (Colossians 2:3). Being God the Son, he, like his Father, is omniscient. To him there are no mysteries. Since he is the Alpha and the Omega (Revelation 1:8, 11; 22:6, 13), no one need inform him of what is to come. He alone has perfect knowledge of what was, what is, and what will come to pass.
Jesus is the source of the glad tidings which an angel foretold at his birth: ". . . I bring you good news of great joy which will be for all the people; for today in the city of David there has been born for you a Savior, who is Christ the Lord" (Luke 2:10, 11 NASB). Jesus is the Christians' example of an euangelistes--the bearer of good news (see Luke 4:17-19).
Jesus is the personification of the perfect pastor-teacher. A pastor leads, cares for, and protects the flock; a teacher provides his sheep with spiritual food as he feeds them God's word, which they in turn assimilate into their spiritual lives. Jesus is the Good Shepherd who gave his life for the sheep (John 10:11, 14). Jesus is a master teacher who through his Spirit instructs his disciples (< L. discipulos, pupil/learner), guiding them into all truth (John 16:13-15).
Gifts as People
Notice that the standard, or measure, to which all Christians are to hew is the Son of God, in whom alone is fullness (Ephesians 4:13). So yes, Christ's DNA resides in the "members" of his body, the Church Universal. All the gifts are embodied in people in ways and in proportions which the Holy Spirit himself sovereignly decides (see 1 Corinthians 12:4-11, especially v.11).
Interestingly, the people of whom Paul speaks (viz., apostles, prophets, evangelists, and pastor-teachers) n Ephesians 4 are themselves gifts to the Church:
". . . He gave some as apostles . . .."
As a conquering general distributes the spoils of war to the citizens for whom he waged and won the war, so also Christ gives these special people to the church as the spoils of the war he fought and won at the cross.
In the wake of his crucifixion and subsequent resurrection, Jesus "led captivity captive" (Psalm 68:18; Ephesians 4:8). As he continues to lead his army in triumph today, his soldiers spread "the sweet aroma of the knowledge of Him in every place" (2 Corinthians 14-17). To those who are perishing, that aroma is "from death to death," but to those who are being saved, "an aroma of life to life" (ibid.).
Gifts as Spirituals (1 Corinthians 12:1)
Just as all the gifts originate and are embodied to perfection in Christ to whom was given "the Spirit without measure" (John 3:34), they are also are embodied in people, however imperfect those people may be. Our Lord Jesus Christ is the source and epitome of the spirituals. He alone is the epitome of
- prophecy (see Revelation 19:10)
- service (see Matthew 20:28; Mark 10:45)
- every good and perfect gift
The Blueprint Is Not the Territory
As for a "blueprint" as to "what the church should look like today" (your words), the only blueprint the New Testament gives us for the polity of each local church (long before the appearance of denominations) is the rule of elders and deacons.
In the first-century churches, there were undoubtedly apostles and the disciples of apostles who exercised leadership in local churches, some of whom were specially called of the Lord to serve a church (or more, as in the case of a traveling evangelist, for example) fulltime (e.g., Paul, Timothy and Titus).
Many, if not most, elders, however, earned a living outside the church (and even the apostle Paul resorted to tent-making when he needed to). The notion of a bureaucracy which exercises leadership and supervision over a network of like-minded local churches was perhaps the furthest thing from the mind of first-century Christians.
This is not to say that bureaucracies and the leadership exercised by vocational Christian workers at denominational headquarters, for example, are anathema to God today. God can--and does--accomplish miraculous works of service through leaders and their followers when like-minded Christians band together to accomplish God-glorifying projects and ministries. God, after all, is not a God of confusion, but of peace (1 Corinthians 14:33), and he expects things to be done "decently and in order" (v.40).
I grew up, for example, within the Plymouth Brethren tradition, and one of the God-glorifying ministries my family and I were involved in was a Christian summer camp for children and families. My father, in fact, was the camp's first Spiritual Director. All told, about 8-10 Plymouth Brethren "assemblies" (our "code" word for churches within our nondenominational denomination!) pitched in to make the camp a reality.
Sixty-plus years later, the various ministries of the camp (which is now a year-round ministry) have seen hundreds (if not thousands) of young people come to faith in Christ and/or grounded in spiritual things, all because the Lord blessed a concerted, collaborative effort of hundreds of dedicated volunteers who contributed time, talent, and treasure to that God-honoring ministry.
In short, in our modern-day fetish for perhaps over-organizing every aspect of church life, whether locally, nationally, or even worldwide, God seems to have been pleased for the last two millennia to bless the efforts of his people, and sometimes almost in spite of themselves!
Are there disadvantages associated with over-organization. I myself have been a member of a church which was run more like a business organization than a spiritual organism, with Christ in charge, and not a minister, a pastor, a bishop, a key elder, or a denominational president.
So many worthwhile and Holy Spirit-inspired visions have died in committees, burdened with unnecessary and overly complicated protocols and red tape.
By the same token, however, wherever there is a critical mass of Spirit-led, Spirit-empowered Christians, God is pleased to bring to fruition what is ultimately His vision for His church, despite the obstacles the enemy of our souls--and sometimes even we ourselves--manage to put in His way. As Jesus said,
". . . I will build my church, and the gates of hell shall not prevail against it" (Matthew 16:18).
God will always be pleased, I believe, to accomplish his vision for the Church Universal through denominations and the organizations they spawn, until the last "living stone" () is added to the superstructure of his masterpiece, the body of Christ. When his masterpiece is complete, the Church in heaven will then
". . . attain to the unity of the faith, and of the knowledge of the Son of God, to a mature man, to the measure of the stature which belongs to the fullness of Christ" (Ephesians 4:13).