This isn't an easy situation.  I'm not familiar with OH law and maybe someone on here that is will comment.  I'd suggest you find someone in law enforcement that will be friendly that you can speak to "off the record" that can give you suggestions as to how to handle this without committing you to a plan of action.  There are cops that are car guys that walk around car shows because they like cars too - see if you can bend one's ear for 10 minutes.  That's one thought.

Another concern: Is one of the parts from the convertible a good convertible frame?   Converts had a very heavy X-member frame for rigidity and without it you really can't build a convertible because building on a coupe or sedan frame yields a flexible flyer that will not hold up.    ALSO, the frame carries the "hidden number" that is used by law enforcement should the car get stolen to verify the VIN number of the car.   When you go to title this new construction, under OH law, they may want to see that number so it may have to match the VIN you will have on your door hinge pillar.

There are many horror stories of professional shops that have built cars from convertible parts along the lines of the project you are describing.  They have led to huge law suits either directly for the seller immediately or for the reseller later or the auction houses that handled the cars if they became big money cars.   We heard about all the high dollar ones.  I suppose the low dollar ones had equal problems on a smaller scale because of lesser dollars.   So this is a word of real CAUTION.   If you can't do this RIGHT AND LEGAL, then I'm suggesting it probably really isn't worth the trouble, because no matter how much you would like to have a convertible now, eventually you will need to sell it.