First, a quick proof of the moral nature of the 4th Commandment:
If a company or a government mandated that its people were mandated to work 7 days a week - I do think that people (in their outrage!) would realize the moral nature of this commandment. Most especially Church Officers, as suddenly its leaders would be very concerned about their ability to draw worshipers to church.
That said, there are a lot of different aspects of this that are being discussed here. I will merely chime in regarding the ceremonial vs. moral nature of the 4th Commandment. Dabney has a very convincing proof on the difference between ceremonial laws and the moral nature of the Sabbath.
"There is another convincing proof that the Sabbath never was a merely Levitical institution, which is found in the fact that in the very law of the Decalogue God commands its observance equally by Jews and Gentiles: "In it thou shall not do any work, thou, nor thy son, nor thy daughter, thy man-servant, nor thy maid-servant, nor thy cattle, nor thy stranger that is within thy gates." This stranger was the foreigner residing in the land of Israel. To see the convincing force of this fact the reader must contrast the jealous care with which the "stranger," the pagan foreigner sojourning in Jewry, was excluded from all share in the Levitical worship. No foreigner could partake of the passover; it was sacrilege. It was at the peril of his life that he presumed to enter the inner courtyard of the temple, where the bloody sacrifice was offered. Now, when this foreigner is required to keep the Sabbath along with the families of Israel, does not this prove that rest to be no ceremonial, no type like the passover and the altar, but a universal moral institution designed for all nations and times?
In addition, you see its observance in Exodus 16:23 before the giving of the Law (in tangible form) on Sinai. You see how the Lord God set apart one day in seven at Creation. You see, our Lord Jesus Christ being proclaimed, "Lord of the Sabbath". If Paul had meant to rescind the keeping of one day in seven as set apart to the Lord, I would argue that we would have as many epistles dedicated to this new doctrine as you would have had with other aspects of the ceremonial system that are being discussed in the NT Epistles for instance regarding circumcision. This is why the Reformed have stressed continuity rather than discontinuity between the Testaments. They are not two separate books, but one Bible and one People of God. As others mentioned, it has become popular as of late to treat them as two different religions thanks to the recent rise of Dispensationalists and New Covenant Theology folks. But we want to see that we share the same faith as our fathers in the Old Testament.
In addition, by spiritualizing the 4th Commandment as "rest in Christ", I would argue that you argue too much for men as "spirits" and not also "bodies". Physical rest is also a component of the 4th Commandment, as is the Spiritual Nature. To force people to work 7 days a week if this is now moral in the New Covenant, is less gracious than the Old. You also pit man's spirit against his body. It is in no way, compassionate.