Been trawling through pages and pages of data, Irish census takings, parochial records.. nothing. Which brings me back to facts based on DNA. So I went through each of the mutual matches that William Dempsey's grandchild (132cM/9segm) and I have in common and to my surprise discovered an outlier; out of the 7 mutual matches, one does not descend from my 2x great-grandmother's 2nd marriage to Joseph Prince, but her 1st marriage to Robert Penn Threlfall.
Of course Ancestry's sadly lacking chromosome browser prevents seeing whether this one match pinged off recombined Prince-Stanton DNA in the other descendants and myself, so I'm still sticking to the theory Dempsey had a Prince parent. The matches combined with relationship prediction tools all point in that direction as well. Here's the genetic and genealogical possibilities based on both DNA and grandparent/grandchild ages: 1900/1962 vs 1901/1965.
*DNA Painter's Shared cM Tool
50% h2c
24% 3c
15% 2c
8% h3c-3c1x
2% 4c-h3c1x
*DNA Segment Tool
52.5% h2c
21.9% 3c
19.9% 2c
3.9% 3c1x-h3c
1.5% 4c-h3c1x
*MyHeritage cM Explainer
40.1% 3c
16.3% 2c
11.8% h2c
3/5% 3c1x
1.5% h3c
What this boils down to in order to narrow search parameters..
*half second cousin (h2c)
Great-grandmother Frances Prince (1868-1950) potentially was a bad girl during her marriage (=1888) and popped out an illegitimate child somewhere among the 'official brood' born in 1889, 1890, 1895, 1897, 1900, 1901, 1903, 1906, 1909 and 1912. Dempsey could've (also) fibbed about his YoB, great-Grams apparently was pretty fertile, and great-Gramps George was on board ships around 1900.
*second cousin (2c)
This means Dempsey is a full sibling of my grandfather. The 5 year gap between child #2 and #3 provides a theoretical possibility. In 1891 great-Grams is listed as head of a household of 2, which includes sister Agnes (daughter Sarah born 1890 is suspiciously absent) but not hubby George, who was off to sea again. She could've been overwhelmed, found herself pregnant, and decided to give up the baby. Who knows. Life sure wasn't easy back then.
*third cousin (3c)
Great-Grams' sibling Agnes Prince (1872-1940), marr. 1894 to Thomas Foster, basically is my main suspect. She's not just the only full sibling that lived long enough to have a child (she and Thomas had 7 in 1895, 1896, 1898, 1902, 1904, 1907 and 1909) but somehow an identical name pops up as William Dempsey's mother in some of Ancestry's trees. And what I've learned from researching the many illegitimate kids in my tree is that they have a tendency to lie about everything except two things: their actual birthday, and the name of their mother. So it's possible some relative actually did order William's marriage certificate, and he had given her real name.
So how does one go about proving the above theories?