Hello!
My 2nd great grandfather is also Michael Hannon, very likely also from Limerick, although I've not been able to confirm this. He was born in Ireland around the same time as your 3rd great grandfather (sometime between 1805 and 1815) and emigrated to the States (Ohio). His first son, Michael Hannon, married an Elizabeth Crawley (in Wisconsin), and his first son (John Edward Hannon) is my grandfather. He moved to Michigan around 1905, met and married my grandmother, Anna M Daly, a member of the prominent Daly family in Dearborn, Michigan.
I don't know if any of this helps but you are correct, most of the Hannons were from the west counties (Clare, Limerick, and Galway). Happy Searching!
Maureen Hannon