Can you please show me the scripture Barnabas is referencing here:
Ye see what is His meaning ; it is not your present Sabbaths that are acceptable [unto Me], but the Sabbath which I have made, in the which, when I have set all things at rest, I will make the beginning of the eighth day which is the beginning of another world. Wherefore also we keep the eighth day for rejoicing, in the which also Jesus rose from the dead, and having been manifested ascended into the heavens.
What is plain is that this guy is searching for a way to switch the day. He is playing Rubick's Bible.
Whoa. You cannot cite this guy as an authority, and then ditch him when he starts to be inconvenient to you.
You picked him as your authority for your assertion that the ECF were Sabbatarians. Now you gotta stick with him.