Surely there are others better equipped to voice an opinion, enarchay. From a theological perspective there’s no obligation, I wouldn’t think, inasmuch as even Jewish Christians are released from the Law. From the gospel narrative we get this:

For this reason the Jews were persecuting Jesus, because He was doing these things on the Sabbath. But He answered them, "My Father is working until now, and I Myself am working." (John 5:16-17)

I’d say that if God exists He is probably still working, wouldn’t you? That would defer the "sabbath rest" of Hebrews 4 to the eschaton. That said, I’d certainly think the church would be free to set aside a sabbath rest, whether weekly or otherwise.