***Paul does not separate baptism from the Gospel***
1 Corinthians 1:17
For Christ sent me not to baptize, but to preach the gospel:
1 Corinthians 1:14
I thank God that I baptized none of you,
1 Corinthians 4:15
...for in Christ Jesus I have begotten you through the gospel.
Looks like a clear distinction to me.
Did you even read my post? The distinction is between the acts of preaching and baptizing, not the Gospel itself and baptism. Baptism is part of our response to the Gospel message.