I don't have a "J.G.Speckman" or "Spectman" in my family, nor a Minnie. My Speckmans descend from Henry Speckmann who came to Massac Co from KY, then IN, and finally settling in Massac Co. in the 1850's.He did have 2 sons named "John"...John Christian Speckman married to an Alvine. John was born in 1837. The other son, John Henry, married an Amelia.
If you have more information, maybe that would help?? Let me know!