Changing Grass Types - Need Advice

Bought a house with a well established landscape including a large lawn. It’s a mix of KGB, Rye, Fine Fescue, and feels like I might as well include Nutsedge as a grass type since it’s all over the place.

The mix feels poorly done as it’s pretty patchy almost like bare spots were filled with one or the other types throughout the years. The patchiness looks terrible in summer as the fine fescue and rye goes dormant. I know the KGB/Rye/Fescue mix is common but I just hate the look and feel. I want a more uniform grass that I know how to manage and treat.

My yard has a large area of full sun and some with partial to full shade. I’m hoping to convert to TTTF everywhere and if needed I’ll add in some KGB for the full shade areas.

My question is whether you recommended doing this conversion over time by overseeding each yeah with the TTTF or is it better to nuke and start fresh with fresh compost and seed?

With the nutsedge issue (and the overall bumpy mess from years of neglected mole issues) I’m thinking of a full restart and leveling but it’s a ton of work that I’m not mentally prepared for.