At first I have to admit it is a bit hard to get around the accent... But I think people recognise that Americans outside of America are the best kind! There is a stereotype of the stupid, fat, obnoxious, ignorant American, greedily wasting resources and believing that the US is the centre of the world. I think a lot of people around the world are pretty fed up of US foreign policy. I suppose there is also an element of neocolonialism as well, with all sorts of US cultural, political and ideological exports pretty unavoidable in most parts of the world now. So I can see what you are saying when talk about jealousy, because it is so easy to see what there is in America and what it does - but personally I think it's a bit broader than that. The US is this hugely powerful and influential country in many ways, which pisses people off - people don't like to have stuff forced down their throats the whole time. Perhaps with British people, it's that US culture is becoming so intertwined into British culture that it is almost usurping it, and because we speak the same language it's so easily accessible to us that it will be inevitable that we get bombarded with it. It's interesting that you blame stereotyping in particular, because although I can see that being stereotyped as an American is the problem for you, I have found that Americans are very prone to generalising and stereotyping when it comes to most things; Americans love to generalise! (I'm not trying to be facetious, but this is an honest observation I have made with many Americans...also the irony was so timely!)
Americans are quite an easy target because we have all these stereotypes about them, but people should get past it. I have American friends and I know that there are a lot of obnoxious people in the UK and everywhere that are going to write off every American they come across, but there are plenty of people who won't as well - lots of British people are really into American culture. I think Americans get teased moreso than a lot of other nationalities (as a nation it's seen as pretty arrogant), but if you just go with it and get some banter going or something, or come off looking quite relaxed about it then people will definitely warm to you! I think a lot of people disagree with US politics because Europe in general is much more left-wing, so I think people will want to know what your perspective is. I hate to say though that if you vote Republican you will probably cement most of the stereotypes that people have against Americans.
One thing, though: make sure you're not too loud, our voices are much softer over here!!