Predictor - andras is right. It wouldn't matter whether there was a daytrading firm in the Turks & Caicos that would take your account. If you failed to report your trading transactions at the end of the year, you'd be committing tax fraud. As andras said, it doesn't matter where your MONEY is - it matters where you are. If you're a US citizen, you're taxed on all your income anywhere in the world. Also note, the IRS monitors foreign wire transfers too. So if you wired a bunch of cash to an offshore account, the IRS would likely end up with a record of it.
But frankly, even if you found an offshore broker to take your account - you'd be taking a big risk. They won't be SIPC insured and you could lose all your money overnight if they folded their tents and vanished.
Now if you bought yourself Belizean citizenship, ...
Good luck.