Interesting that a gun store or FFL has accepted proof of residency from you, most won't accept ANY form of ID of any sort unless it is issued by a government agency.
I would also say that the Ohio BMV has the firm thought that you should obtain an Ohio driver's license, given your situation. Legally, I am not certain, but the Ohio BMV would prefer the revenue that they could get from you considering how long you've been here.
Lastly... I doubt that any Ohio Sheriff is likely to issue you a CHL without proof of residency, and I bet that your driver's license will be the main topic of conversation.
I'll be interested in hearing how this develops. And for what it's worth, although the law and the rules are (or should be) clearly defined, the Sheriff that you deal with won't necessarily execute things properly.
I like to swap brass... and I'm looking for .32 H&R Mag, .327 Fed Mag, .380 Auto and 10mm. If you have some and would like to swap for something else, send me a note!