The very same Thomas, but new data. A family of Roman Catholics, possibly from Ireland, is listed in the Landsburgh Lists of 1822 in the Saltcoats Town section of the Parish of Stevenston, Ayrshire. This informal, personal census of the Reverend Landsburgh's own C.of Scotland parish includesR.C.John McAvoy, wife Elizabeth Campbell and 2 children not named plus an unidentified lodger.
Further, I find the 70 yr old mother listed in the mid June 1875 Brooklyn census with Thomas and his family (her name is at the bottom and the corner of the page is torn off!) could be the 80 yr.old Elizabeth McAvoy who died in late June1875. There are no ther elderly Elizabeth or any other given name females who die bet 1875 and 1880 except this one. By 1880, Elizabeth is gone.
Have the grave list from Holy Cross in Brooklyn, but the others in this grave have surnames I don't recognize--Keyes and Burke.