WHO has been DNA tested? There is a price war, the cost now $100 or less. Especially as we aren't sure who are brothers, cousins, etc., DNA testing may be helpful. I was tested by Family Tree DNA (though you can test from one company now and upload results to other companies, or GEDmatch takes all results). I presently have NO Hassett matches, though I have over 10 matches to Moore, my gg-grandmother Mary Hassett Moore.
Catharine Batterby Hassett is my most distant known direct-line female ancestor (mtDNA). My haplogroup via her is K1c2.
The men many be able to use Y-DNA to connect brothers & cousins.