I’m from the UK and I feel like I’ve heard enough UK English speakers saying “quote” that I had never thought of it as an American thing. That isn’t to say that the distinction you make doesn’t exist though, just that it may be variable across demographics or contexts.
Tangential, but I don’t understand why in American English you feel the need to say the word quote at all. In UK English we just use intenation.
Can I quote you on that?
It’s useful for when you’re quoting someone who happens to use the exact same intonation as you!
I’m from the UK and I feel like I’ve heard enough UK English speakers saying “quote” that I had never thought of it as an American thing. That isn’t to say that the distinction you make doesn’t exist though, just that it may be variable across demographics or contexts.