Hi, Susan! First up, it's important to note that the information about Chromosome 1 has nothing to do with Dan's Q-M346 yDNA haplogroup or your grandfather's Q-M3. The Chr 1 information is not in any way associated with Native American origin.
And, odd as it may seem, the Q-M3 clade is actually four branches deeper--or newer--on the yDNA haplotree than is Q-M346. Q-M3 shows a good deal of evidence of being linked to indigenous peoples of the Americas, but Q-M346 is about twice as old, as in more than 30,000-35,000 years old, and can't be construed as being Native-associated without further yDNA testing to refine the subclade. If Dan and your grandfather come from the same patrilineal line, Dan is almost certain to be Q-M3 also. If he and Lloyd are of the same patrilineal line, that Dan is reported as Q-M346 and Lloyd as Q-M3 just points to a deficiency of relying on autosomal microarray tests to establish yDNA or mtDNA haplogroups.
The known pile-up area on Chromosome 1 being referenced is from loci 118,434,520 to 153,401,108. You can see a bit more about it (and read about what pile-up regions actually imply) on the ISOGG Wiki, or read the original 2014 research paper at PLoS Genetics. That particular range is shown as representing 9.95cM. There are 386 known encoding genes within that area, which means the genes-to-base pair ratio is about 40% more dense here than is the average across the genome.
I think I might wonder about the 26.84cM shown in the results, too. If you were to do the comparison at GEDmatch, I'll bet you get results that more closely agree with those from Rutgers University, 19.5cM sex-averaged...which is how the centiMorgan is always estimated and reported to us. Looking at the segment from the perspective of your female genome it's actually 29.5cM, but from Dan's perspective it's only 10.1cM. Since the 9.95cM pile-up region comprises about 78% of the shared segment with Dan, that also seems more in line with a ~20cM segment rather than ~27cM. (More on the vagaries of cM estimation below.)
The segment on Chromosome 1 is large enough by any evaluation to possibly be genealogically meaningful. That said, it entirely encompasses that known pile-up region that's been found to be 19 times more prevalent than would normally be expected in GERMLINE Europe samples, and 33 times more prevalent in GERMLINE Asia. The net message is that, in my opinion, you shouldn't discard matches on that segment, but you should consider the DNA as possibly being far older--think a continental population level here--than something you can realistically use as solid evidence for genealogy.
In other words, you're likely to find a number of people with whom you share that pile-up region, but who don't share any of your family tree going back many hundreds of years. Using the GERMLINE Europe frequency numbers, in fact, as few as 1 in 19 matches might be genealogically relevant. That's the pitfall of a pile-up region: it can look like genealogical DNA evidence, but in fact that piece of Chromosome 1 may date back 20 or 30 generations and not be usable as evidence for an MRCA.
Relatedly (no pun intended 
), I can't tell from the question if you're hoping to use autosomal DNA to locate the biological parents of someone born four to six generations back from you, or if the ancestral couple would be your 4g-grandparents to 6g-grandparents. The first instance may be doable, but quite challenging. The second is, in my opinion, unlikely to happen. At least with any evidentiary accuracy; the pile-up regions being only one roadblock. And pile-ups occur not only at the continental population level, but also at the haplotypic level...meaning your ancestral family multiple generations ago. I advise anyone embarking on triangulation exercises farther back than a 2g-grandparent always start by compiling his or her own haplotypic pile-up map. Genetic genealogist Debbie Kennett wrote an excellent article about it: https://cruwys.blogspot.com/2018/01/small-segments-and-pile-ups.html. It's possible to do without a specialized application; you can use spreadsheet software and the data you can get from most companies (alas, AncestryDNA being the notable exception).
A core issue is that, with our current, common testing technology, the usefulness of autosomal DNA pretty much peters out at the level of 4g-grandparents, or 5th-cousin test takers. At that level we're dealing with theoretical sharing amounts below a meaningful threshold for comparison. The centiMorgan is far from being an accurate measurement: it's only a very broad guesstimate that uses decades-old computation methods and relies on the imputed accuracy of the population sample used to estimate DNA recombination rates. These rates can vary considerably by continental-level populations, by the version of the genomic map in use (our current DNA tests are using a map that's one major and at least 13 minor releases old) and, as I noted, by the inherent inaccuracies of averaging the male and female genomes. Too, new research is constantly causing us to revise our notions of recombination "hotspots," which then affects how we estimate recombination potential across the genomic map (some research-paper links for those who are having a lot of trouble sleeping: Nature Communications, Apr 2017; The Royal Society, Nov 2017; Nature, Sep 2018). Referencing Rutgers University again, their interpolation for a 10cM segment has a standard deviation of 1.2cM...meaning that 95% of the time a reported 10cM segment will be at least 7.4cM.
With solid paper-trail genealogies plus detailed research, diligence, and multiple test-takers, you might be able to triangulate back to 5g-grandparents. But until we get to the point we can compare actual, individual nucleotide values through whole genome sequencing, the centiMorgan will remain too imprecise to use beyond that. If there is no paper-trail at all, as with unknown parentage, I'd guess that trying to get to 2g-grandparents would be reasonable, but 3g-grandparents a stretch.
