Well, it may work okay. You have one big thing going for you--they want to keep you and your dollars at the school. So, they may want to make this flexible schedule work out.

This is weird to me:

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They were also concerned because at 4 she's very tall (she wears a size 6 so her pants will reach her ankles), but she's thin (we love adjustable waist pants).

So they don't want to advance her because she's thin? Hmm, maybe we should hold my 3rd percentile DS back a grade...

FWIW, my DS, who is socioemotionally mature, goes to 1st grade for a good chunk of his academic day but stays with K for specials, lunch, recess, yoga and dance, etc and seems happy with this. I mean, I think he would also be fine in 1st, but he likes the "fun" "play" elements of K. As he should, because he's K age.