Your challenge is to create a situation in which a large scale Ulster Unionist element and sentiments can arise within the United States either alongside or displacing the OTL large scale Irish Nationalist/Republican element within the US.
As famous as the US is for Hibernophilia, there are lots of Anglophiles as well. I was just speaking to a friend last night (neither of us having any ancestry in the British Isles), and he declared his preference for Unionism and of, ideally, all of Ireland as a constituent country of the UK.
I'd wager that if asked, you'd find a lot of "soft" Unionists like this in the US.