Paddy, I've lived in Ohio but that doesn't make me an authority by any stretch of the imagination.
However, I think you're very safe with staying with 1 March 1803 as the date Ohio was made a state of the Union. While the odd technicality is interesting, Ohio materially functioned and was recognized as a state from that 1803 action forward. Full rights and political representation as a state--and its residents began paying federal income taxes along with all other states when those came to be in 1912--means that Ohio has been treated as a state since the U.S. Congress approved its admission in 1803.