Frankly, I think the Sabbatarian argument is baseless. Nowhere in the NT are Christians commanded to worship on a specific day. Nowhere in the NT are Christians forbidden from worshiping on a certain day either.
It is incorrect to call Sunday 'the Sabbath' but it is also incorrect to claim that Christians are wrong to worship on Sunday. Further, I don't accept the argument that the first day of the week is the day on which Christians are to gather. That's just what they happened to do in the first century, but saying that we "must" is making doctrine from narrative, which is always suspect.
If it works for your fellowship to meet on a Thursday afternoon, and you spend that time in the Word, in song, in prayer and fellowship and the breaking of bread, but don't meet on Saturday or Sunday, is that somehow wrong or inadequate? Um, no. Not a bit.