DOES Anyone know where I could take a S&W armorer class
in Ohio?

Check with the S&W Academy......

Academy & Training | Smith & Wesson

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Ret. LE, FA Instr, S&W Armorer

Apparently the default link at the S&W site takes one to the LE & Miltary classes by default. Further research indicates that they do have civilian classes and you can enroll with or without your own toolkit.

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Who watches the watchers?

It has been a long time since I last attended one of their classes but I believe when you register you can purchase a took kit from Smith that they will have there at the class for you. Contact their training section and they can fill you in on all the details.