I've been reading this thread with interest as I know next to nothing about my ancestors in Straid and Ballynure, but the last post made me prick my ears up, as part of my family was Park.
Probably no connection as William was born in Straid in 1831, and married Margaret Strange in Ballynure in 1851 so a couple of generations before the people you mention, but what struck me was what a very very small world it is on this site!