Well somewhere along the line you switched the topic from "sabbath observance" to "synagogue worship".
Sabbath observance can take place in a synagogue, in a house, or down by a river:
Act 16:13 And on the sabbath we went out of the city by a river side, where prayer was wont to be made; and we sat down, and spake unto the women which resorted thither.
No synagogue. No jewish ceremonies, but coming together on the sabbath.
The question has always been whether or not the sabbath was observed by Christians. The answer is of course it was.
Paul believed in the sabbath of God. To state otherwise goes against his word in God inspired scripture:
Act 24:14 But this I confess unto thee, that after the way which they call heresy, so worship I the God of my fathers, believing all things which are written in the law and in the prophets:
Jesus believed in the sabbath, created through him and for him:
Mat 5:17 Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfill.
Mat 5:18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled
Luk 6:5 And he said unto them, That the Son of man is Lord also of the sabbath.
Mat 12:8 For the Son of man is Lord even of the sabbath day.
Again, a prime opportunity for Jesus, God in the flesh, to state to his followers that the sabbath is no longer in effect. Does he? Nope, he AFFIRMS the sabbath by reminding us that he IS the LORD of the sabbath. He is reminding them, and us, that it is HIS sabbath, his creation.
And as previously pointed out, there is not one hint of controversy in scripture about a decision to NOT observe God's sabbaths.
You have tradition and culture on your side. Fortunately I have a commandment of God, the testimony of Jesus Christ, the testimony of Paul and scripture on my side.
You keep saying this, but yet you cannot point to any Scripture that shows baptized Christians, both Jews and gentiles, in a Christian worship setting on the last days sabbath of the Jews. The fact that Paul was able to find a place where people gathered on the old covenant sabbath to pray does not enjoin Christians to worship on the sabbath of the Jews. We have already shown it was Paul's custom to seek them out on their worship places in order to convert Jews to Christ.
It was also Paul's custom at one point to have his hair cut off to take a vow in order to not be falsely accused by the apostate Jews. Have you made this your custom as well? Should all Chrisians cut off their hair when they take a vow?
Nowhere do we see baptized gentiles observing new moons or annual feast days of the Jews.
Mat 5:17 Think not that I am come to destroy the law
Since you are so sure that Matt. 5:17,18 authorizes the keeping of the last day sabbath, and since none of your old covenant sabbatarian friends has chosen to answer my challenge, why don't you take a crack at this list:
Do you bring your grain offering to the local priest (Lev. 2:1)?
Do you bring your tresspass offering to the local priest (Lev. 5:6)?
Do you avoid temple worship when you have a "discharge" (Lev. 15:2)?
Do you get your tonsorial fashions approved by a priest or rabbi?
Do you have your sons circumcised by a rabbi?
Do your women bring a purification offering to the priest after bearing a child (Lev. 12:6)?
Do you bring your skin ailments to the priest for adjudication (Lev. 13:4)?
Do you bring cases of adultery to a preist to be tried by "bitter water" (Num. 5:19)?
Until you can honestly answer these questions about old covenant practices, your quote of Matthew 5 to support the old covenant sabbath rings hollow.