Quote
Dealing with what the statements you provided mean in context is something to be done by someone other then myself

Exactly, God alone works baptismal regeneration when it pleases Him without any cooperation from man.

Quote
we'd still be lacking the Scriptural warrant to believe in what the possibility would allow.

We have God's promises (Mark 16:16; Acts 2:38; Acts 22;16; Rom. 6:3,4; Gal. 3:26, 27; Eph. 5:25, 26; Col. 2:12; Titus 3: 5; and 1 Peter 3:21). What more do you want?

Quote
To be clear, the supposed possibility would only be meaningful if my preconcieved theological construct required that I believe in baptismal regeneration.

Good point! How can someone be regenerated in baptism, when they reject the possibility that baptism could be efficicious? Similarly, how can someone be regenerated through preaching, when they do not believe in the possibility that preaching could be efficacious?
Quote
Are you able to show to us that your belief is not based upon this, but rather Scripture?

I have already given you ample evidence from scripture which you have chosen to ignore in order to persue doctrines based on man's reason not scripture.