Eibhlin, there is some confusion on this family. Much of my data comes from Frank Ashe, son of James P. The marriage date of 27 Jan 1857 for J.A./C.P. I found myself in the Dingle books back in 1976. Robyn Coghlan of Australia also has provided me w/information--her husband is descended from Brigid Ashe, daughter of J.A./C.P.; Brigid & Nora were sent ahead to Australia w/the rest of the family planning to follow. Economics of the time changed then, making it more practical for the rest of the family to go to the US, but why Buffalo, am not sure. Anyway, here's the dates I have given me by Frank or Robyn:
John Gregory Ashe 23 Sep 1826 Minard-d. 9 Aug 1892 Buffalo
Catherine Prendiville 20 Feb 1844-17 Dec 1916 Buffalo
Mary Ashe 4 Apr 1858, did not migrate; m. Patrick Curran
Brigid Ashe 14 Nov 1859-1913 Adelaide, South Australia, m. John Sweeney 20 Dec 1883
Nora Ashe 9 Apr 1861-27 Apr 1945 Australia, m. 10 Feb 1880 Thomas Riley
Johanna Ashe 5 Mar 1863
Catherine Ashe 10 Feb 1865-1928; m. Samuel PEck 1884
Margaret 6 Jan 1867, m. Cavanaugh
Elizabeth 15 Apr 1868, m. Evans
Gregory 2 Nov 1870
Ellen or Helen, 17 Dec 1872, m. Harrington
Anna Ashe 11 Apr 1874-Jan 1969, m. Charles Henry Smith 17 May 1902 Greenfield, MA
John Michael Ashe 29 Sep 1876, m. Anna Hand 20 Sep 1911 Buffalo
James P. Ashe 11 Feb 1879-1960, m. Catherine Sheridan
Thomas Ashe (now deceased, formerly of Dublin & Kinard East) --you've probably seen his Ashe family chart--said that Gregory came to Minard, married Bridie Kennedy of Coole, Anascaul.
The Ashes are a tough family to research as they were so prolific, and I personally think they were more than one family. There's simply too many around to have been one family. It's a mistake to jump to conclusions and say that this particular Gregory (or Matt or John, etc.) is the same as another, when there are not enough records to substantiate the data previous to the 1820's when the Dingle books were started.
Let me know what you think of all this--am particularly puzzled by the dates for Catherine's children given in the 1900 census you cited--it appears to be the right family because of the grandson mentioned.