Henry Wood - DNA Connection

I just discovered I have a distant DNA match with the sister of singer Buffy Sainte-Marie, Elaine 'Lainey' (Sainte-Marie) Mixter. Our match is on Gedmatch and shows we have MRCA 7.7. I found her on Ancestry and her attached tree shows this line continued to use the Atwood surname down to her maternal grandmother Elizabeth (Atwood) Kenrick, a descendant of this Henry and his wife Abigail.

I came to Geni to see if I could find who my common ancestors with the Sainte-Marie children is. I see in their tree that they have Henry's parents as John Atwood and his wife Joan Coleman, both from England.

I'm sharing this because I'm also a direct Coleman descendant, so my connection 'could' be a Coleman one. However, I also have Atwood cousins in Mississippi, not sharing the Atwood lines but they have the surname Atwood and we share other common ancestors married into their Atwood line.

Lainey Sainte-Marie's Ancestry tree doesn't have enough information included for me to see any other pathways I may be related to them on so if it's not the Coleman / Atwood line, I have no clue. And it threw me a bit when I came to Geni and see that the entire line is listed as Wood rather than Atwood on this site. I don't know which is correct. For what it's worth, here are the parents their tree has for this Henry:

Father:
John Atwood
B:4 Feb 1582 - Christened Sandusted,Field,Surrey,England
D:27 Feb 1644 Plymouth,Plymouth,Massachusetts,USA

which matches the father connected here on Geni.

Mother:
Joan Coleson
B:1587 Westminister,,Middlesex,England
D:1654-06-01 Boston,Suffolk,Massachusetts,USA

Of course, they could have errors in their tree...