Sorry if I misunderstood what you were looking to do.
As for transferring the judgment, all you have to do is get a certified copy from the court clerk and then file that judgment with the court clerk in the county you're wanting to enforce it in - - such as Franklin County.
The only issue you'll have is that you can only enforce the judgment in Franklin County IF he (1) lives there, or (2) owns/has property there. You mentioned that he works in Franklin Co., so you would be able to file the judgment there and then issue a garnishment to his employer for payment of his income until paid in full. There are several Ohio counties online that have forms available for garnishment, such as the following one: http://www.franklincountyohio.gov/clerk/CivilForms.cfm. Your county likely has similar forms you can use.
However, if your ex does not live in Franklin county, you could not seek to hold him in contempt of court OR execute on his vehicles through another county. Instead, that would have to be done through the county where he lives/where the property is located.
Thus, you CAN transfer the judgment simply by getting a certified copy and filing it in any county you wish. However, the court only has jurisdiction over the PERSON if he lives there and over the PROPERTY that's located within the county.
I hope this clears up the issue, and I apologize for misunderstanding the first go round.