Cheerful hope you are back on the road and DD is ok?
Like Tabula with her normal speech I cut out many Irish phrases and terms when posting, but my normal spelling is British spelling. I have to consciously drop Us out of words when I write in the US. The DCs poke fun at me and mispronounce words like colour
when I write them.
However, I feel a bit strange using the word Mum and Mummy except in reference to my own mother -- I couldn't imagine myself ever calling her Mom, whereas I am Mommy to the DCs (for some reason they do not use Mom at all even thought they are now aged 13 to 24. DS has a completely non-mother related name for me, which is odd, though he sometimes calls me Ma).
Hats and fascinators at weddings are considered very British. I have never seen any at American weddings (mostly RC) and they were never a thing in Ireland either except for CofI weddings, though my mother has been to a few weddings recently where the mother and grandmother of the bride had a hat. I hate hats. I have never managed to find one that didn't turn me into Worzel Gummidge.
I think in the case of Frasier it was just bad writing in the case of 'gotten', but elevator is a word you would learn to use very soon after arrival (probably in the airport) so I wouldn't fault them for that. Around here, got is used far more frequently then gotten. As far as things British went, imo the worst sin of Frasier was different British accents for Daphne and her brother, but this wasn't something my DCs noticed at all.
I would never call Americans dumb -- maybe they are victims of a bit of patronising though?
I do think there is more language traffic from west to east than east to west however.
British TV is hot in the US. I became aware of a fanatic little Doc Martin fan club among mothers in DD4's school two years ago, and DD4 and the computer lab teacher used to chat about Downton Abbey during lab time. Doctor Who and Sherlock are taking over the world, with no concession to non-British audiences that I can see. I wonder if some British speech will creep into the US as a result.