Improving conditions of a tenure-track job offer
Your question, "how should I argue my case?" is unanswerable without a statement of what your "case" is. With any job offer, you state what you want, and the other party agrees or disagrees. A vague feeling that you should be "recognised a bit more" doesn't matter. What is it that would make you more likely to take the position, or make it more likely that, given the position, you'd be successful at it? Also: Congratulations!