Below are some notes from another diligent SMITH researcher in my husband's line - Jo Sparks.
"For a long time (1950's-abt.2005) another SMITH family researcher - Vera Groover - was 'the' accepted authority on which SMITH families in Dawson & Lumpkin Cos., GA were related to whom.
However after some diligent research, in 2010 I challenged my own acceptance (since 2002) of Vera Groover's assumption that John & Polly (Montgomery) Smith were the parents of Thomas H. Smith my(& my husband Terry's)GGF."
Jo indicated to me that she has been able to prove the parents of Thomas (GGF to my husband & to Jo) should be WILLIAM & SARAH SMITH. Her notes and photos of William & Sarah,also one of Thomas & Elizabeth, are in my gedcom.
At this time I am still not sure how your John & Andrew Smith fit in with our SMITH line in this area of GA. Not much is known about the siblings of our William &/or Thomas Smith. Perhaps w/ more work we could find out for sure.
DNA testing could definitely be helpful. If your line & my husband Terry's are close 'kin' at all this type of testing would show it. Terry had his male DNA tested by Family Tree DNA a couple of years ago; and their database is getting rather large by now. It's really very interesting. A very reliable 'tool' in helping to ID our ancestors. Have you had your testing done yet?