Don't talk salary again until you get an offer. That's the moment where you have maximum leverage: they're all internally aligned on hiring you over anybody else, they just need you to say yes. You'll need to clean up the mess you made with your original answer - "I know I previously said $X was fine, but after doing some more market research, I see that $Y would be a more appropriate salary because <list of reasons from your market research>." In the future, if you want to maximize your freedom to negotiate, don't spit out a number or a range! But recruiters do need to know that your salary expectations are aligned with their budget, or the whole interview process could be a waste of everyone's time.

Yeah definitely wait until the offer stage to bring it up again, there's always time to tell them your situation has changed and the previous number isn't applicable anymore. Just be careful how you do it because you don't want to price yourself out of the offer and have your recruiter pull it.