I discovered
http://en.wikipedia.org/wiki/Hiberno-English.
This exactly solves the problem I've had with my main character. I found a bunch of stuff I was doing right, indicating that I'd picked the right path. A bunch more things that I was doing almost right, in particular, the difference between "be" and "is" that no longer exists in modern English, but adds a distinctive component to the character's dialog. A few things I was doing wrong. A bunch of things I wasn't doing at all. And a lot of great words I can salt into the text.
I have three books and one course on this subject, but this Wikipedia page is the most useful thing I've found yet.