Random Writing Question

When I write, I try to use the grammar and spelling that the person who's narrating, or whose POV we're occupying would use. So, American characters use American terms and spelling, and UK/Commonwealth citizens use British terms and spelling, regardless of whether the fandom is American or British-based. For characters like Edwin Jarvis and Peggy Carter, who are Brits surrounded by Americans in an American setting, I sometimes run into problems with what the dialogue of the Americans around them should be spelled like. For example, when an American is talking about his mother to a British person, does my British narrator record him as having said 'Mum' or 'Mom'? Because there is a distinct sound difference there, and it's hard for me to imagine any American saying 'Mum'. Airplane or aeroplane is another one.

It's probably something I'm overthinking, but I do feel like reading dialogue where Tony Stark says 'Mum' takes a person out of the moment a bit.

Any thoughts?