I don't think Paul could have meant what you've written above based on the grammatical structure of the verse.
In
1 Timothy 1:15, the word "sinners" is a substantival adjective, or an adjective that functions like a noun (The Greek word is
hamartōlous. Therefore, as a noun, "sinners" is essentially a broad term category covering all sinners (as in, "Jesus Christ came into the world to save sinners" coupled with Paul's earlier teaching that "all have sinned" from
Romans 3:23).
Secondly, the Greek for "of whom" is Genitive (possessive) and plural. So, what Paul is saying (as I understand it according to the grammar) is, of the broad term category "sinners", I was the foremost, or number 1.
Paul is ranking himself. It doesn't mean, that in the eyes of God, Paul actually was, at the time of his writing, the worst sinner in an entire world of sinners, but we don't get God's opinion of Paul in the verse, unless the Holy Spirit specifically inspired him to describe himself that way for a legitimate reason.
Otherwise, I think Paul is merely expressing himself to his son in the Gospel, Timothy, in the way he currently understands himself. It's not a pity-partying call to self-condemnation; rather it's an acknowledgement that if Paul is going to judge anyone in the world as a sinner, the only one he's going to so label is himself. He's not trying to make comparisons between himself and every other sinner in the world. Rather, it's his way of not judging any other sinner as worse than himself or more deserving of divine wrath.