Well, I think you may be out of luck on this one (see below). I retract my previous comment.
I would ask to renegotiate the terms of the non compete to be very specific with regard to your job there. And try to get rid of the 1 year after clause.

If you were only prevented from CFI'ing somewhere else while working there, that would be reasonable.

If they think you are a valuable CFI, and you could work somewhere else right now, then let them know they will lose you over this agreement as written. Try not to burn any bridges.


My Employment Lawyer - Non-competition Agreements in Ohio - History and Law

"In Lake Land Empl. Group of Akron, LLC v. Columber, 101 Ohio St. 3d 242, 245-246 (Ohio 2004), however, the Ohio Supreme Court held that continued at-will employment was sufficient consideration to support a non-competition agreement. The Court viewed presentation of a noncompetition agreement by an employer to an at-will employee as, in effect, a proposal to renegotiate the terms of the parties' at-will employment. As a result, an employer can require non-competition agreements from all of its employees and can terminate, without legal liability, those employees who refuse to sign."