Truly fascinating. I feel that it can't be coincidence Anthony Kelly worked in Doolough with Arthur Shaen Bingham, and Edward Kelly had connections to Major Denis Bingham. Perhaps a positive relationship, but I can't be sure how Edward might link in with Anthony. The absence of records makes it speculative - all I have is an elder Anthony Kelly (c.1838-1911) and his wife Annie Carey (c.1852-1935). They had big family, and Anthony was fifty odds when his last child was born - Rose Kelly (1889-1949). Young Anthony's wife Ellen O'Donnell died young, and he was left struggling. In the end Rose gave him a house with lottery winnings, and his people came over to Scotland too. On old Anthony and Annie's wedding, we have a woman named Rose Kelly as witness - perhaps Anthony's mother? Nothing more - for all I know Edward could have been a brother. It then implies a Roscommon origin - from these records you posted - and not a Mayo origin. That's really quite interesting for us. Hope more is unearthed here.