I can't help you with the Adcock family that you have posted here. I can tell you a little something on the James Adcock & his wife Elizabeth you mentioned.
I have suspected for some time that this James Adcock was a brother to my Thomas Adcock. They are both listed together on numerous deeds buying and selling lands in Columbia, Richmond, & Hancock counties, namely on Keg Creek. In one of the deeds they both are listed as selling land adjacent to John Adcock, land that was originally granted to Thomas Adcock on April 5, 1785.
Thomas & James Adcock are the only 2 Adcocks that I have found that were granted Rev War Bounty Land Grants for fighting out of Georgia.
I have not yet been able to make a connection between Thomas & James Adcock, and the John Adcock whose land was adjacent to theirs on Keg Creek. I have a hunch that they are somehow related to this John Adcock, but have not been able to prove this, and may never be able to. Though it is ironic that these Adcock people were living right next to each other on Keg Creek in 1788.
I believe that this John Adcock was related to Edmund Adcock and from the Adcocks from Virginia.
My Thomas Adcock and his son John Adcock both drew blanks in the 1805 Bounty Land Grant and they left Georgia and were in Baldwin County, Mississippi Territory (later Baldwin & Monroe county Alabama) by 1806.
Interestingly, another line of Adcocks also were in more Northern parts of Alabama around 1816-1820.
Hope this is somewhat helpful on this James Adcock you mentioned.