Before I tell you any advice, I think that you should know that some Amercans find an accent incredibly sexy. I can understand that you want to blend in, but don't beat your self upabout it if you can't completely perfect your accent.
Okay, now, to improve your accent I think it might be beneficial if you watched material that had both American and British accents being spoken side-by-side. I think it would help because you could kind of "compare" the accents, almost side-by-side, and the differences might stand out more if you hear an American accent saying something immediately after you have heard a British accent saying it. The only thing I can think of right now is the movie "Marie Antoinette" directed by Sofia Coppola, which has actually been criticized because it has a mixture of British, American, and French accents.
You probably know these colloquial abbreviations and conjunctions, but I'll put them anyways just in case. You should probably have a person with a native American accent tell you how to pronounce these, since they would probably sound really odd pronounced wrong :
kind of =
kinda (pronounced
KIND-uh)
the = (pronounced like "
thuh word", though NEVER spelled this way, and sometimes, even "
th'noun")
sort of =
sorta (can be pronounced either
sor-duh or
SOR-duh)
What do you, What are you =
watchya ("Watchya think?" "Watchya going to do?") (pronounced
WUT-chya)
What do you = can also be called
whaddaya ("Whaddaya going to do?") (pronounced
WUH-duh-yuh)
doing = doin' (pronounced
DOO-in)