C.K.
You can pull your kid anytime you want!
And in MN, the "compulsory" age for school attendance isn't even until 7, which your bio says your daughter is now.
I am very pro-homeschooling, for all the reasons you list in your post, and so many more! Academic readiness is only a small part of a child's progress in school, and as you've pointed out, maturity and other social issues are overlooked. (Just push 'em on through like cattle!)
I don't know your work/home situation, but if this were my kid, I'd pull her TODAY, and homeschool for the rest of the year. I'm still researching homeschool protocol myself, but in MN it's a matter of filing some paperwork with the school district you're in, which includes your lesson plan.
Even if homeschooling long-term is not an option for you, it would buy you time until the next school year starts. You could research schools and not feel rushed and stressed about the whole deal.