The OP has a 529 that he owns that he can use to pay some of that gap. The problem is that if he uses it this year to pay that gap, the amount has to be reported as untaxed income to the student since he is the noncustodial parent. Them’s the rules. That would hem reduce aid in a subsequent year.
So, in order to optimize financial aid AND the 529, the 529 should be used to pay the gap right before senior year. Then OP can pay off up to $10k in loans out of 529, and so can the student when 529 then turned over without affecting any more FAFSAs.
I know non custodial parents in similar situations. But without a 529 in place. If they pay the tuition or any expenses on behalf of the kid, that’s supposed to be reported as untaxed income on the FAFSA which causes a gap. If the divorced parents are not in synch, no one wants to trust the other parent with outright cash gifts which could solve the problem as gifts to student’s parents not reportable on FAFSA