Hi Matthew,
I tried the same process with the new family.
The 1870 & 1880 censuses have the family - Patrick born 1835 + - 1 and Eliza born in Ireland also.
Frustratingly, on rootsireland.ie there are 22 Patrick Fagans born 1835 + - 1 in all counties including 6 in Meath.
Assuming Patrick & Eliza married in Ireland, there are 2 marrriages on rootsireland.ie 1860 in Westmeath and 1861 in Dublin. However as Eliza was born in 1843 - 1 (from the census) she would have been only 17 or 18.
The marriages on ancestry has a record of Patrick Fagan & Eliza Dwyer 5 May 1867 in Massachusetts. On this her age is accurate with his a little out.
However, the year fits well with the first child, Alice born 1869. Others were Edward 1872 Mary 1876 & Frederick 1878
Parents on the marraige record: (his) Edward & Mary hers Timothy & Alice
Of course there are no birth records on rootsireland for Patrick & Eliza with these parents!!
You can google Tithe Applotments (1823-27) and search for free - there are 455 Fagans from Westmeath Meath Cavan Longford mainly.
Hope this helps a bit - maybe Pat who replied above can track him can track him with the birth year of 1835/36.
Col