Tom, I want to take a minute to help you understand autosomal DNA a little better.
You wrote your ideas here:
> Ancestry drops the accuracy 50% per generation because there are fewer makers to sequence from the original 22 genomes at each stage. Fewer markers means lesser accuracy since at that level scores and even hundreds of different surnames are identified, so even at six generations the makers values may be the same for scores of surnames, which is why as you say that the DNA washes out.
https://www.geni.com/discussions/169645?msg=1158311
There is more there, but this gives a basic idea of what you are saying.
You seem to be picturing autosomal DNA as being like yDNA. But autosomal DNA doesn't have markers or STRs. It's not linked to surnames. It's accuracy doesn't drop by 50 percent each generation.
Erase those ideas. Autosomal DNA looks at segment matches. On any particular chromosome you get 50 percent of your DNA on a chromosome from your mother and 50 percent from your father. Over the generations the segments get broken up through inheritance. So, with any particular relative you might match one or more segments of different sizes (measured in centimorgans (cM).
The number and size of the segments you share with someone is a rough guide to your actual relationship. For example, with different aunts I share 1838, 1597, and 1436 total cM. Our longest matching segments are 132, 128, and 108 cM, respectively. With my half-sister, about the same genetic distance, I share 1894 total cM. Our longest matching segment is 159. The ranges are reasonably predictable. Any could see from these numbers that these four women are probably aunts, nieces, or half-sisters.
For genealogical purposes, we normally look only for matching segments that are 7 cM or more. If you drop the matching threshold below 7 cM, you'll end up with many more matches but they are likely to be "population matches". That is, they are just background noise. You really do match, but the segments aren't large enough to be meaningful.
So, you see. No markers. No STRs. No surname links. The accuracy doesn't drop at all. It just becomes harder to find the source of the match until eventually the match is so small (weak) that it "washes out".