Can you move her for the start of yr 3 in September, and drive the journey needed temporarily until you sort the house?
School first, house second.
I moved our daughter from a not so good school on the not so good side of town, again, a cock up really! Then, moved her start of yr 2, last year, to a great school in a great area, across town. Yes, she has to deal with it, and bless her, she did! She was amazing.
We drove past the school, a lot, saying how pretty it was, how it had a huge park behind it and well go there everyday, and they have hot school dinners, infants and juniors mixed so our daughter would see her younger siblings (unlike the old school) All those little things, really worked for our daughter and she so so excited. The first day was unforgettable, as in the guilt we suffered.... But, we knew within a day or two, we had done the right thing for us as a family, 3 kids, and we had done the right thing for our oldest daughter.
To help her settle, in the first few weeks we had loads of play dates at our place with cousins and old friend's kids, just to make sure she felt secure that she had good friends. Then, we began to have play dates with her new friends.. We even had a huge halloween party for all the girls in her class.
Then, although planning on renting, the perfect house came on the market 0.3 miles from the school. So, it all fell into place, bish bosh!
A year on, we're living the dream.
Go for it. Just pave the way.... And, bribe away. Do it!