Is it possible to be tired of your accent?

When I was in China the thing that made me different was on display for everyone. Didn't bother me to be different because so many people around me were different. Everyone could spot me "not being Chinese" about a bazillion miles away and that was ok cause no one expects to blend in China when they are so pale their skin could potentially blind people. 10 months of winter will do that to you.
Unfortunately I seem to blend in in Australia on first observation. And then... I speak. The one thing that makes me so different is instantly on audio display for the whole world.And it really feels like stereo surround sound without the cool graphics at the theatre because in the end all you get is... a Yank.
Phone sales people start entire conversations with me about my accent. In shopping centres the people stare and ask and away we go. Meeting other mothers at school is always a matter of jumping through the hoops of my accent and what on earth I am doing here. Which is a realllllly long story. I have no 5 second answer to that question yet. Imagine everywhere you go looking like almost everyone else and then opening your mouth and it's like your entire appearance miraculously changes. And now I really feel like I am whining because my husband stands out where ever he goes no matter what he does and there remains some little hope that someday my accent will tune into the Aussie radio station I know is buried inside me somewhere there is little hope his height is going to lessen in any significant way. I am sure of it!
Americans are not, I think we all know, extremely well loved in the rest of the world and it would help if I could disguised my unsameness somehow. It would be inevitable though that my fake Australian accent always comes out sounding like Audrey Hepburn's Eliza Dolittle.
I think I could handle all of this but after the first few months being able to predict what most people are going to ask 2 minutes after you say hello is bound to just make you tired of not being a little more like everyone else. I am not annoyed at them. Not at all. I quite happily agree that my muddled accent, came from China, can't pick a place to say I am from is probably confusing for the average Aussie considering it's confusing for me.
If I could sound just a bit more American it might help. I have always thought it was obvious that I was a Yank and I will still stick to my American guns and say that most Aussies are just being polite and trying not to hurt a potential Canadian's feelings when they ask if I am from the other North American country instead of asking if I am from...The United States of America. Very important to say the whole country's proper name because a lot of people do that here as well. I promise The States is perfectly ok.
Anyway I thought they were just being nice until a women married to a Canadian was 100% sure I was Canadian so maybe next time I should yes. They are more mysterious, nicer, and they have national health care. Not a bad place to be from if you can't pick a place anyway.
So overall I would just ask that sooner or later I either sound more American or at least begin to manage a decent Aus. Please don't rain on my parade. I don't want to be 70 years old and be the cute little Yank married to that big bloke down the street.