Oooohhhh! My heart beat faster when I read the part of your message that said..."Family lore is that John left home, was gone about 5 years and when he returned home the family had left. (Nobody seems to know where he left home from.)
And then as I continued to read on...."My great uncle said, that they lived in So and No Carolina either before or after John was born- lore is also that he hunted all over and never found the family."
I have heard that same story before. When researching my husband's fathers ancestry, I found he descended from a Joel Adams a Florida resident who had migrated from the Carolinas. I traced these Carolina Adamses back to Bedford County, VA. It seems they were originally part of my own grandmother's Adams family. But this particular clan had left Virginia for the Carolinas, then later generations migrated farther south into Florida.
I sure hope this tiny piece of "Adams Puzzel Info" helps you out in the search for your own John Adams. If you decide to investigate this further, I can offer what I have on them. Just let me know.