You guys do realize that she doesn't have to legally be on the lease as long as you aren't breaking any housing laws correct? The only reason you add someone to the lease is to give them permission to
1. Submit work orders
2. give consent to enter to management
3. allow entry in lock out situations
4. split liability with the complex for any damages or missed rent.
Why anyone is making any kind of deal of her not being on the lease is beyond me. She had a verbal lease with you, she paid her part of the rent, she technically owes you another 30 days of rent if she wants to play hardball.
Her stuff is there, take pictures of it. Mail is not the only thing that confirms residency in the state of Ohio. Her stuff being there, her paying you rent and her having a key would confirm residency, therefore would validate your verbal contract.
These are all very straightforward, simple, landlord/tenant laws in the state of Ohio. You don't need to lie about squat.