I am looking at switching to private schools for grade 5, including a grade skip with the switch. DD would be in grade 1, with the private school provision of 9/1 birthdate deadline for K. Yet, will consider her for a skip after a few grades.

I wouldn't get the skip in public school. It is an expense but I have known people who got into the private school and then ended up with financial aid. So you may want to see if it is a good fit and then try to get them to help finance you after the first year. I find strategy is a big part in getting our kids the education they need.