Jill, this is strictly a shot in the dark, but let me give you a 'speculation.'
I'm assuming that your great-grandfather John Pine was born in the 1870s or 1880s if his son was born in 1911.I know that a John Pine of Gloucester County, NJ (abt 1752-1818) m. Hannah Hiden in Philadelphia and died in Bedford, PA.They had at least six sons: Lazarus III (named for his grandfather, b.1784; Jacob J. 1788-1856, d. in Champaign County, Ohio; John 1790-1861, d. in Lawrence County, Ohio, Jonathan; James 1798-1834, d. in Champaign County, Ohio; & Gilbert 1799-?, m. Sarah Baggs in Champaign County, Ohio and migrated to Illinois . Gilbert & Sarah had at least six sons, as well (James, William, Henry, George, Benjamin, and John).All these were b. between 1832 & 1845.Any one of them could have had a son or even a grandson born in the 1870s or 1880s, and John seems to have been one of the favored 'family names' in each generation of this clan.
So, perhaps it is within this clan that you might find your ancestry.
I think that's all I have on this line, but you can findit at Familysearch.com