Just one trans woman's opinion, but I hold that the ideal way to recover from accidentally misgendering a person and being called out is to simply repeat the sentence, corrected. No apologies (or just a quick "sorry" or "pardon" if it flows), no justifications. It happens. We get it. Nobody's looking to shame anyone, only correct a mistake before it perpetuates.

A: "And then he told me that he wanted to..."
B: "They"
A: "And then they told me that they wanted to meet me at this coffee shop..."