Be sure you mention the restraining orders and DYFS, and that he hasn’t paid court ordered support in your request for waivers for non-custodial parent profiles at CSS profile schools. I wouldn’t talk about his diagnosis or finances with schools — just that you and your kids have no contact, the info on the orders/DYFS, and the non-payment of support.
If he could raise his verbal score, he’d have a better shot at schools that might meet his financial need.
I don’t think a kid with a 650 verbal has a shot at UChicago.