Re: 1000 yard shooting ranges near cincinnati.
You can shoot at Ft. Knox. The Kentucky State Rifle and Pistol Association is authorized to run shooting tournaments there, and, typically they schedule four or five 1000 yard NRA governed events each year. You can Google them for match entry details.
Shooting under match conditions, with target pullers in the pit, allows for call/strike analysis. This is important if you want to become a real good long range shooter.