Further thoughts -

Phil Kelly's Placenames lists Loughan ny Maidjey, meaning "Plank Lakelet", in the parish of Michael. This is probably Lough ny Masha, or Lough ny Mashey, or your Lougham my Madjey, correctly spelled.

I wonder if "Breggan" could be "Creggan", a rocky place. There is a Creggan Doo, Black Rocky Place, listed by Phil Kelly in Michael. Or possibly, Breckan, meaning Speckled Place, although Phil Kelly does not list one in Michael but there is / was a Brecknagh in Michael.