Lizziel.
There are so many situations where you will not be a DNA match with a 6th cousin but will be a goodish match with someone more distantly related.
Standard advice is to test as many of your relatives as possible - siblings, parent, cousins etc., then to try and persuade them all to upload to Gedmatch.
I was hoping to be a match with 5th cousins descended from our mutual 4G grandparents, but no match appeared. No other matches appeared on this line at all - had I made an error with parentage? Then I found a match with a 6th cousin, descended from previous generation in that line, my cousin is a match with 7th cousin from the same line.
Of course, at ancestry there are the limitations that you cannot see exactly where you match without a chromosome browser.
It may be the case that you need a DNA match at each generation, 'proving' that each child has been assigned the correct parents.
Wikitree provides examples of their standards of assigning DNA evidence.
https://www.wikitree.com/wiki/Help:TriangulationI assign a DNA icon as main picture in gallery at ancestry, then in pedigree view, looking to see where an icon is missing, then perhaps use the surname or place search to see if I can find any appropriate matches.
Most of my 2G grandparents now have an icon attached.
DNA is an additional tool, doesn't replace paper trail. Go with your paper trail, until and unless you find evidence to the contrary - absence of DNA matching, especially at this distance, is not evidence.
Regards Margaret