Miscommunication is one of my favorite shenanigans. Love reading it. (And your character designs are beeeeaautiful, by the way.)
I'm from Deep South USA but somehow managed to have a distinctly un-Southern accent (most people think I'm from Oregon). Due to this, I've always set my stories in the South, but have always had significant difficulties writing my characters to sound like they're Southern.
I tend to stick with understated accents. I don't often spell out mispronunciations. If it's important that a character has an accent, I usually just have someone point it out-- in one of my comics, there's an old Scottish guy who gets ribbed for his accent occasionally, which luckily works very naturally with the cast. I figure my readers are probably smart enough to pick it up if that's the sort of thing they find interesting and would like to know.