We must pay 3 months of tuition to a 501c3 private school for early withdrawal. Any way to turn that (we get nothing in return) into a tax deductible gift to the school?

No, it's not a contribution. It's the same as paying tuition. And the school is not going to give you a receipt for a contribution.

REQUIRED payments can't be contributions as you are not making the payment of your own free will.