This is me as well. I am proud to be American, but I also forget that I am one on a day-to-day basis. I just don't think about people's nationalities as I go about my grocery shopping or squeezing my way on the tube.
And because I am used to hearing an English accent, I don't even think about my own. So if I do ever get teased for my accent it takes me a moment to register why it is different. I actually really struggle with accents in general now. The English sounds familiar to me, as did American for so long, so if I hear an actor on TV that I don't know, I cannot always tell if they are English or American.
This is me as well, especially with the accents. I've often thought I just have a 'dead ear' where accents are concerned, because I don't recognise American accents! After nearly 4 1/2 years here, I'm starting too though.
Maybe it's because I work in an office with people from all over - Russia, Africa, Brazil, Malaysia - my American-ness is rarely commented on - we tend to sometimes concentrate on discussing how different are lives are from where we used to live, but that's about it.
Weeks can now go by before someone somewhere gives me a hint that they've noticed I'm not from here - whether that's coming out and asking where I'm from, or that sudden head turn that tells me someone's reacted to my accent...which tends to still make me feel momentarily self-conscious. It is those times I don't forget I'm American, or maybe it would be better to say that I'm reminded that I'm different and don't quite fit in.
But, all of the rest of the time, I know I DO fit in and it has nothing to do with my nationality.
IMO, whether one is trying to de-Americanise or not, one does lots of different things to fit into their new lives that they would never have done in the US. For me, it has been learning a lot about the history of the place I'm in - not just Birmingham, but the whole country (but I've been doing that my whole life where the UK is concerned anyway). I think it is this conscious effort that has made me feel even more attached to my new life because none of it has been instinctive (you know, like in the place where you were born and brought up?), it has all had to be learned...