I have not researched John Brady, I read some about him online by the verifying, thorough genealogists and looked at John Brady's Big Island Township, Marion County, Ohio censuses. I noticed that Christopher Brady and John Brady both have children named Lavina and William.
I did not see a John Brady in the Marion Co OH Land Patents.
It would be interesting to see DNA at 67 Markers by descendants of these two Brady man.
Best wishes in your search,