I am a novice at this type of reply, but----. I have no direct knowledge of 
Elliot but there was a John Eggleston who married Elizabeth Elliot in 1763 in Edmondbyers.  At this time there was a large Eggleston family in Stanhope, which is not far over the moors. John and Elizabeth had four other children christened in Edmondbyers.  Elliot Eggleston and Ann Walton had a child in Edmondbyers in 1792, with subsequent children 
christened in Stanhope in 1803 and 1806.  What is your Eggleston 
connection?