A couple years ago, Michigan State offered my daughter a near full tuition scholarship (would have cost about $4-5k per year). They also offered $10k per year room/board scholarship (but only to extent she lived on campus). Seemed odd to me they would offer a taxable scholarship (room and board) when they were not covering full tuition. Ultimately, I think they were counting on you moving off campus (or not being able to getting into on-campus apartment junior/senior years) and thus forfeiting portion of room and board scholarship. Total cost would have been about $7-8k per year after scholarships. Not sure if that has changed since.
Ohio State has moved away from merit aid in recent years toward need based aid. Various levels of merit scholarships have been reduced $500-1,000 a year. Eminence still offers full cost of attendance. But its given to about 25 kids per year. About 75 get interviews. Very competitive.
Both are worth a shot. Good luck to you.