Hi! An early congratulations!
I haven't been to Graham Elliot, so cannot comment, but have been to all of the others. Kiki's, while romantic, just doesn't have great food, in my opinion. I don't think it's in the class of your other options. Avec, with it's wonderful food, is casual, noisy, and doesn't take reservations. I think your suggestion of a Sunday dinner at Avec is good - you won't have quite the crowds on a Sunday. It's just not the place I'd want to go after getting engaged (waiting for an hour plus to bump elbows with your neighbors might not be the right choice). I think Spring, Blackbird, and Sepia are all good choices. Blackbird probably has the edge on food of the three, in my opinion, but Sepia might be more romantic and memorable.
If you want delicious, French, romantic, and only a semi-splurge, I suggest considering Bistrot Campagne in Lincoln Square, especially if you can get an outside table. It's my favorite relatively reasonable French spot in the city. Amazing pork chops.
Feel free to ask for more advice. The folks here are really friendly and know their restaurants.