This is actually where we disagree. If we have to do something to accept "the gift" it's earned. We did something (obey, be baptized) for "the gift". It ceases to be a gift.
The verses you cited can be easily explain that baptism is one step in the regeneration process. Hence the writers were only discussing just step "X" of the regeneration process. We obey our Lord Jesus in baptism because He has changed us to want to do so. And, yes, this is what the Bible clearly states as I pointed out with the case of Cornelius which you have not yet explain. While its important to review the doctrinal text, God also gives us Biblical examples to ensure our accurate interpretation. Most people fail to examine these stories closely and match them to other text to understand the workings of God.
I don't wish to sound mean spirited; I'm really a swell guy. But given my past experiences with people who hold this view, I doubt if we're going to change each other's minds on this.
I have given an explanation to the case of Cornelius, you have just yet to comment on my explanation. I have shown, in the Bible, that baptism is for the remission of sins. Until you can prove to me that we are saved before our sins are remitted, then you can't prove that salvation happens before baptism. Period.