Phillipa, a chara,
Your reference to the anglicized 'Shule Aroon' being sung during an American war is close. It was originally popularized during the American Revolutionary War (and it was also sung during the 'War Between The States' as that particular conflict is referred to here in the South). Buttermilk Hill is located in Jackson County in the State of Illinois. Many veterans of the Revolution are buried there and it is a much revered and visited place.
Thank you so much for giving us the words in Irish. You're a wonder and a gem gan praghas! -- Áine