I haven't heard of any problems at the Alliance rifle club. In fact, Mike fortune has sent me pictures of them breaking ground for a 1000 yard berm (the range was previously limited to 600). Alliance is in mid eastern Ohio.
Another option is Miami Valley Rifle and Pistol down near Cincinnati. They have 600 yards there. I don't think they have dedicated F-class, but you could probably get away with it in their 3x600 prone matches. They have a varmint league that shoots thru the winter and spring.
Depending on where in Ohio you live, you might want to check out Camp Atturberry just south of Indianapollis, IN. As a resident of Dayton Ohio, I've found that Camp Atturberry is the closest 1000 yard range to me, at just over 2 1/2 hours drive. They shoot across the course on saturday, and long range (1x600 & 2x1000) F-class and prone are welcome.
Where in Ohio do you live?
-Bryan