We considered making a similar arrangement with a private GT school. They were low on enrollment, so they were happy to work with us. We chose to go another direction--a co-op, and then ultimately part-time with the school for homeschoolers--but the GT school was quite willing to work something out with us that would suit our needs, with the tuition to be prorated.
I suspect a school that had a waitlist wouldn't be interested. But if numbers are low, I'd bet a lot of private schools would consider partial enrollment.
