There's an old, Hadmaid-unrelated video interview on Youtube with Max where he talks mostly with his natural, English accent and then upon request switches mid-stream to an American accent, although at a significantly higher register than Nick talks. He mentioned he's only ever played American characters, and of all the aspects of acting, switching accents is the least difficult for him.

Here's the video starting at the relevant part. (It's from 2011, wow, baby Max!)

As for Nick, there was one scene (S02E06?) where, upon rewatching with my sister the other week, I swear I noticed his accent slip the tiniest bit. Would have to rewatch to confirm, though.