I am interested in this same individual. A William Adams, born in 1700's in North Carolina, and married to a Mary E. also from North Carolina. The had a son named George W. Adams, born in 1804 in North Carolina. He is my line.
I am not sure about some of your facts though. As we all know from during this, the info is sketchy at best, and often muddled by time and poor record keeping in the early years of our country.
My main problem is with the math. If William was born in 1763, and died fighting in 1815 (war of 1812) he would have been an "old man" by the standards of the time. People typically didn't live as long back then, and weren't normally called to defense at such an advanced age. What sources did you gleen this info from?
Otherwise, I woulld be interested to share any info with a possible distant relative such as yourselves.