www.Rootsireland.ie for the 2 Tipperary "branches" show no Thomas Haneys +/-5 years of 1841. It searches a wide variety of surname spellings but excluded Heaney.

I tried that and found 2 different Thomas Heagnys born in Lorrha, one in 1840 (Patrick Heagny & Anne Connell) and 1842(John Heagny & Bridget Costello). No addresses.

Your problem here is that you don't have much to go on and Tipperary is one of the biggest counties in Ireland.

Did Thomas have any children to help find other names in his family? If so, have you DNA tested his descendants?