I was interested in your posting as I believe my great great grandmother was Anne Dunne born near Rochfortbridge (Mullingar) near Piercetown. She married Thomas Eighan and they sired my great grandmother Elizabeth Eighan.
Elizabeth married John Leogue and one of their daughters, Katherine emigrated to the U.S. and married a man by the name of Duffy in Boston. I am now wondering if she knew him before she left Ireland. I did not know the Duffy name came from Westmeath.
Moate is in Westmeath and there is a Heritage Research Center located there.
The Dunne name spelled with the "E" is very common in Westmeath. I looked through my files but could not find a Bridget in the time frame that you are looking for.
I have not heard of Montrath but then there are a lot of places that I haven't heard of.
Hope this is of some help. Good luck.