I thought that they got it onto a regular basis in about 1811 and it worked well from then on (which rather agrees with the last line of your post), but it is not a subject I've never explored - I was just relying on secondary sources such as Fortescue for this.
Isn't there a book specifically on the Irish Militia? By McAnally (? query spelling?). I've never looked at it, but I'll add it to my list as it might have a bit of what I'm looking for.