Cue Sheets: How do you avoid the last-minute delivery panic?

Hey everyone, Mei-Lin here. I'm currently a Production Coordinator on a pretty tight-turnaround series of spots, shot mostly on an ALEXA Mini with a couple of days on an FX6 for some b-roll. The edit's coming together, but the cue sheet always ends up being this monumental sprint right before delivery to the client. I've tried compiling music info as we license tracks, but then things shift in the edit, or we swap out a piece, and it feels like I'm constantly backtracking. What I'm really struggling with is building it organically throughout post. How have you personally integrated the creation of the Cue Sheet into your post-production workflow to avoid it becoming a last-minute crisis before delivery?