Hi Lynn: I am a descendant from Joseph to Isaac to William P. to Charles Raymond (my grandfather). I have also been searching for lineage before Joseph 1771. I came across some info given to me by other relatives and think I've maybe found something. It is a poem written by John C. Houston (Lovell, Wyoming) who writes about his grandfather, Joseph (Isaac's son who became a Mormon). I believe it describes where these Asay's came from, if you follow the poem. Do you have a copy of it? It is called "Family Trails" and it starts out:
Living in the Fatherland long, long ago,
The Assayes joined with the French Hugenot.
The very earliest knowledge history tells,
Their homes were in the city of Aux-La-Chappells.

If you would like a full copy (it's about 130 lines long) let me know.

Are you of this lineage also?