I think the way to go is to give sparing hints at the accent - occasionally write the words as they sound, and try to indicate more with syntax and context. Open up a copy of Trainspotting for an idea of how inpenetrable writing an accent can be. Or read just about any comic with Gambit in it. *sighs*

I found The Curious Affair of the Dog in the Night-time to give a very readable first person view of a boy with Aspergers - I don't know how accurate the depiction was, but I certainly had an idea that he didn't view the world like the characters he was interacting with.