The Opera district is a super fun and nutty area the wander around in. The window shopping is amazing and even though crowded, the big department store in the area is a blast to wander through. Consider doing a tour of the opera building, if you can manage it. (You’d need to call as I don’t think they do tours on performance days.)
Montmartre is another area that’s fun but definitely only go during the day time and be cautious of which metro you get off at. Rick Steves ain’t kidding when he says some of the area around there are dicey. We went in 2015 and the area had enough military around to make it feel safe but per my parents, who were there in March, it feels a little less so now. Maybe someone else can corroborate.
I know you said you are a little museumed out but two less crowded/less visit but seriously amazing museums are the Marmotten (all the Monets you could ever ask for without the crowds of the Orsay or Orangerie) and the Cluny. The Cluny is the medieval museum. It contains the seriously beautiful unicorn tapistries and a ton of great art, furniture, and statues. It is one of my favorite museums in the city. It’s undergoing renovations currently but I think it might be due to reopen in time for your trip. And Napoleon’s Tomb at Les Invalides is a worthwhile stop to me. The Army museum is cool before if you haven’t been.
Consider just taking a stroll through some of the great gardens too. The Tuileries up from the Louvre to the Egyptian oblisque is nice but also consider exploring the Luxembourg Gardens or the Jardin des Plantes.
It also may sound cheesy but no matter how often I’m in Paris, I still always do a river cruise. There’s nothing like seeing the Eiffel Tower and Notre Dame from the Siene. Notre Dame is always a must for me and Sainte Chappelle as well. Going super early in the morning when it opens is awesome. You’ll be with maybe 100 people tops and it completely changes the experience. That’s when I finally understood why ND is so amazing. I know you said your churched out as well but there are some truly amazing little churches in/around the 6th and on Ile St Louis. The Paris RS book gives a pretty good account of those.
If you decide you have time to spare, getting out of the city for the day could be worth it. Most people book it to Versailles but why not visit some of the less crowded/visited chateaus? Fontainebleau is a ramshackle history lesson (get the audio guide) and then there is my all time favorite chateau (this is coming from someone who was in the Loire in May) Vaux le Vicomte. It was the inspiration/reason Versailles was built. Both are an easy train ride away and can actually be seen in the same day, even using public transport alone,, if planned carefully. But if I had to pick only one, I’d pick Vaux (get the audio guide).