Again, I'm not preaching against baptism, and if someone claimed to be saved by faith but refused to be immersed I'd have my doubts. But one shouldn't put the cart either in front of or beside the horse. The Bible is clear that faith results in salvation which results in baptism, not that faith plus baptism results in salvation.
Again, look to the thief on the cross, who did nothing save to put his trust in Jesus hanging next to him. To try to parse that down according to "which" covenant was in effect is to miss the point--in all covenants, righteousness is only obtained by trusting in God (Gen. 15, Rom. 4).
I have only one response to this, and it is something I have repeated on here several times, and I will make this the last one.
The Bible, which is the Word of God, is trustworthy. The Bible states that baptism is for the remission of sins (Acts 2:38). In the Greek, this is the same exact structure as is used in Matthew 26:28, where Christ says that His blood is shed for the remission of sins. I don't think you, or anyone, would ever dare say that Christ did not shed His blood for the remission of sins. And yet, you claim that baptism is not for the the remission of sins, even though the exact same language is used in both cases. That, my friend, is a grave misuse of Scripture.