I’m the exact person they want for the role (confirmed by the team) and they couldn’t find an adequate replacement for me the last time they looked, which is why they upped the range for the salary and went back to me a year later.

That right there is your strongest bargaining chip. They want you, specifically, and are having trouble filling the role without you.

Be willing to walk away and let them know that. My old employer had a zero negotiation policy. I was not able to negotiate. However, my manager was very much in a situation where they needed him more than he needed them and guess who was able to negotiate a substantial salary bump? He was more than willing to walk away and they decided they'd rather have him than not. Smart businesses will move mountains for the perfect candidate.