Thanks to the Wells poster, good info to have!
People like our middle - School Without Walls at Francis-Stephens. The good thing for your daughter is that it's Prek-8 so she could enroll as soon as you move and then she wouldn't need to adjust to a brand new school for middle. Worth at least taking a look if you have another high school plan up your sleeve. The feeder high school, Cardozo, is not worth moving for (understatement of the year!!)
I have friends whose children currently attend and really like CHML's middle, which can be accessed from anywhere in the city. Classes are tiny. But getting in requires lottery luck. CHML has DCUM detractors, for what that's worth.
From what you describe, though, the Latins sound like the best fit. Wish it was a sure thing!