I would submit that Jesus doesn't have any claim on the culture and does not want us to "reclaim" any portion of it. His claims are on us as a whole. That means that we are not even at liberty to create a culture apart from Him, let alone go out and find a reclamation project to present to Him. He has not sent His disciples into the world to create a culture of a particular type. The great commission has no such mandate.
It is Jesus Himself who will cause all things to be brought under His feet. When you read 1 Cor. 15, it is clear that everything that is put under Jesus' feet is not what it was before then. What He submits to the Father is what exists after all dominion, authority and power are destroyed. That will include, lock, stock and barrel, culture(s).
I respect Schaeffer and others who subscribe to this idea that Christians may improve the world by their Christian conduct and witness. There was a time when I agreed. I just don't now. I believe I was wrong. Without argument, there are many qualities of living that are more appealing with the presence of a greater Christian witness, but that is not why we're here. It is not only not enough, it is a whole missing of the mark, a hamartia to get downright theological about it.
C.S. Lewis wrote that Satan skillfully uses two false propositions with one of them having a greater appearance of truth to it so as to lure people into choosing one of them. For Satan, that's a win/win. For us who are in Christ, it is a loss either way. A pagan world or unbelieving world versus a world made better by Christian conduct and witness are both Satan's lair. Jesus did not come to save this. He came to destroy it and set in order an entire new order of things that He insists that we conform to now and promises us that He will burn away the veneer of the corrupted order as it now presents itself to us. Faith is, at least in part if not altogether, trusting Christ to do exactly and just that, for that is the whole of His plan (isn't it?).
I know that John 3:17 says that Jesus did not come into the world to condemn it but to save it. That means simply that Jesus entered the world and brought the Light of God to the darkness of men. He said, also that they were condemned already who did not believe Him (no need for Him to condemn them when they --- and their culture --- were already condemned). The "saving" of the world is the redemption of the creation according to the promise of God. God's creation will not be destroyed, but the fallen order of things will be.
That's extensive. The order of things. Every way in which we perceive reality is through "the order of things". There is only one order that reveals to us Truth, and that is the one, single Order of Truth that is revealed in the person of Jesus. All the rest is ..... well, culture. And, culture is fallen, fallen. It is tilting at windmills to "reclaim" it.

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