Thomas Shimmin & Ann Cottier were the parents of Wm Shimmin who married Jane Crowe 28 Nov 1846 (Patrick). Parents of Thos Shimmin were 'probably' Phil Shimmin & Cath Quine - still trying to prove this, maybe next step is Land Records (winter project!). Can't conclusively identify Thos or Ann in 1841C:
1841 'Ballacosnahan' Thomas (age 45) m. Cath Quayle (of German)
1841 'Ballacain' Thomas (age 45) m. Ann Fayle (of Marown?). Had son Thos bp. 1 Feb 1818 (Marown) - poss. candidate for husband of Ann Cowley?
1841 'Mullin-y-Cloie' Thomas (age 45) poss. husband of Ann Cottier - sister Cath Key & dau. Ellinor Shimmin on same page maybe?

Thomas Shimmin & Ann Cowley
I think Thos's age on JoDaviess tombstone is 31 not 91. Would also tie in with 1841C listing Thos age 25 lead miner, Ann age 25, Eleanor age 3. Son Philip age 1 poss with g.parents John & Eleanor Cowley.

Ann Shimmin & Thomas Moore
Ann Shimmin, dau. of Phil Shimmin & Cath Quine m. Philip Quine 12 Nov 1808- Pat. May have settled in New York. In Phil's 1822 will he mentions daus. Anne Quine & Sarah Moore (m. Thomas Moore 13 Dec 1808-Pat).
Candidates for your Thos Moore & Ann Shimmin in 1841C & 1851C are at Ballakerka, Patrick - Ann listed as from 'German' (poss. parents Nicholas Shimmin & Jane Killey?). Their dau Ann Moore bp 11 Nov 1821-Pat. Parish Register says ' rec'd into the church being one year and 11 days old' (I believe this is the Ann Moore who marries Robert Watts.
Hope this is of some help.