Well I looked at one of my family's old scrap files (put on disk back in 1991) and found this census listing:
Alexander, J. W.WM40FarmerTNTNTN EWF33Wife A.J.WF12Dau S.E.WF10Dau M.E.WF7Dau A.J.LWM5Son M.B.WF3Dau J.T.WM1Son D.J.WF60MotherTNNC? 1880 Henderson County Tenn Census Lists: #83-85
J.W. and D.J. match the names you listed.I don't know though if it means we're related because the person who was doing my family's genealogy research at the time was doing a lot of 'name finding' without showing much to link names together.
My great-great-great grandfather's name was Harvey J. Alexander.His wife was Martha.They had, I believe, 8 children together (including Harvey M., my g-g-grandfather).
Harvey J. was born in 1809 in North Carolina, from what I've been told.He moved to Madison County, Tennessee with his wife Martha and their children.
Madison county is right next to Henderson county.I was under the false belief that my family just lived in Henderson County (from what I can gather, they do live in the Lexington area, I just don't know who they are).They also live in the Jackson area of Madison county.
The reason my family is so out-of-touch with each other is because of that fire in Jackson back in the late 1800s and also because my grandfather (Leroy Alexander) and his brother (Truman Alexander) moved down here to Florida together and the family's been pretty well split up since.
It could be that J.M. and Harvey J. could be brothers or cousins and they both could have moved to Tennessee from North Carolina (just assuming that your family was from there at some point).....just like my grandfather and his brother did when they came to Florida.
Let me know if any of this helps.Sorry I didn't have much to go on.If I find anything, I'll post a reply on this thread.