Acts 20:7 and 1 Corinthians 16:2 doesn't seem to support your theory nor does the early Church Fathers (Justin Martyr, Tertullian, etc...).
Also, Apocalypse 1:10 calls it the Lord's Day which is referred to in the Didache (14) "On the Lord's Day come together and break bread. And give thanks after confessing your sins that your sacrifice may be pure."
Jesus was made known in the breaking of the bread on the of the day of the Resurrection (The Lord's Day) on the road to Emmaus.
The counting of days of the week by the Jews was based on the weekly Sabbath not upon festival Sabbaths which wouldn't square with not getting everyone confused.
Why shouldn't Luke 18:12 then be translated as "I fast twice a Sabbath: I give tithes of all that I possess. "?
Acts 20:7, J.P. Green/Concordant Version
1Cor 16:2/Concordant Version
Luke 18:12/Concordant Version
Since you must be new to pre-Catholic history, I would point out that "Lord's Day" in Revelation 1:10 is a reference to the weekly Sabbath before paganism and anti-Semitism took over Christianity. Of course after this well known political change, propaganda was developed to de-judaize the NT documents.
Luke 18:12 means that they skipped two of the three meals on Sabbath. Jews are supposed to feast three meals, but some extra pious Jews skipped two in order to study and pray. Eliezer Segal of the U. of Calgary explains how some extra pious Jews fasted on Sabbath.
There is no evidence of a connection between the "first of the Sabbaths" and the rare Jewish counting of days to the Sabbath you reference. That's like saying that because monkeys and man share 98% DNA that they must be related.