I am a Gentile believer that has strong convictions to observing the law when possible. besides that I don't know whether or not I am anything else.
I honor your desire to keep Torah as best as possible.
Well, as for whether you are a Gentile or Hebrew Messianic; I don't think it much matters, really. I don't think G-d has a first and coach class when it comes to Torah keeping, excepting those things explicitly written to Israel.
Once you were “not a people,”
but now you are “God’s people.”
You were shown “no mercy,”
but now you have been shown “mercy.” - 1 Peter 2:10 TLV
As for whether we feast or fast on Shabbat— well, it's complicated.
There are several things to consider.
1. Moses' seat (Matthew 23:1-7)
While groups I respect like First Fruits of Zion use this to justify tradition
(see
Is the Jewish Calendar Wrong?), here is an indictment about doing just this sort of thing (adding impediments). Yes we should whenever possible consider tradition when it is good, reputable, edifying (Phillipians 4:8) we must not let minhag interfere with that to which G-d calls us individually or, especially, greater Torah observance. (Mk. 7:13)
No, there is no biblical proscription against fasting on Shabbat. In fact,
some early sources suggest that it might have been the norm at one time:
https://people.ucalgary.ca/~elsegal/Shokel/021031_SabbathFast.html
Y-shuah fasted for 40 days and 40 nights; so did Moses —AFTER he had been given the Torah! (no mention was made about taking 5 breaks in-between)
However, later Rabbis declared it to be inappropriate to fast on a day that is to be welcomed as a delight, "The Bride." (And yet Isaiah 58 seems to be talking about Yom Kippur, which we are to call a "delight") So there you have it. And it brings us to the next point.
2. Messianic Unity, or the "Hinei Ma Tov" principle.
(Romans 14)
If your community celebrates Shabbat in joy, then explicitly fasting on Shabbat because in the 1st century "it may have been the norm" is just being oppositional. I don't think that you are doing this, but consider this:
Jewish custom prohibits mourning on Shabbat, but if a brother or sister is mourning a loss and needs encouragement, fast with them! (Romans 12:15) Better is showing compassion on a member of Messiah's body than keeping the traditions of men!
We are also not to cause others to stumble and should always act in consideration of others (previous verses listed. see also 1 Cor. 19:19-23; 1 Cor. 8; 1 Cor. 12:25-26)
3. Now the Lord is the Spirit and where the Spirit of the Lord is, there is liberty. - 2 Corinthians 3:17 WEB
I would encourage you to read 2 Corinthians 3 and Colossians 2 again.
First what Paul is NOT saying: he doesn't say to NOT keep the feasts. But where there is no law against such things, there is freedom. Freedom to what end? To follow G-d!
If you are struggling with sin, and G-d calls you to fast, what better way to find intimacy than during his appointed time to meet with Him?
Some sins are particularly difficult to talk to others about. (The wolf would like nothing more than to get a sheep off on its own.) I sincerely hope that you are able to find someone of such righteous character to be able to "confess your sins to" (James 5:16) that you may be healed. And if they are willing to "mourn with those who mourn", they should be able to fast and pray with you, even on Shabbat.
(P.S.: Unless you have a word from the L-rd, you may want to wait until 2nd October 2018, because it really is a mitzvah to rejoice for all the days in this holiday. [Leviticus 23:40] )