Thanks for doing some serious detective work.You have found a Joseph Carrol born in the some year as our Joseph Carroll (the alternate spelling is in the ballpark - we have much more drastic alternatives).
This could be our guy but we would need a whole lot more data to establish that. He certainly could have remained in PA when his parents moved to Tennessee and Lancaster Co. PA is not that far from Lycoming Co.PA. I had assumed that he moved to TN with his parents in 1867 but he easily could have been on his own at age 19.
It would be interesting to see an 1890 census to compare the birth place of Joseph's parents as declared there. Our Joseph's parents were definitely from Delaware Co, NY.It would also be interesting to see an 1870 and 1880 census for Kingston Springs, Cheatham Co. TN to see if Joseph is listed there.
Thanks for chipping in to help.If you have access to the census records above I would appreciate it if you could check them out.