Thank you, buzzy2, for that very informative post.
I am not a lawyer, so don't take this as legal advice, but just as layman's speculation, I can imagine three potential workarounds.
a) As briefly mentioned in the article buzzy2 provided, travel to some foreign country that allows this and open an account at a foreign stock brokerage that never solicited you. I am not a lawyer and I haven't read much of the relevant regulations, so I am just guessing that that foreign brokerage would not be in violation of US law because they never solicited your business, which I am guessing is important because I am also guessing that paying someone to break US laws is itself defined as a US crime somewhere.
b) A legally more elaborate approach might be to buy an existing foreign corporation and trade through that (since it was not ""FORMED by a U.S. person principally for the purpose of investing in securities not registered under the Act") [1]. This is my favorite, since one would have a wide choice of stock brokerages to use, it would be easy to switch or to pick one that offered access to exchanges in many countries, and one could continue living in the US perhaps without even having to travel to set this up. I would, however, want to make sure that there was no common law saying that buying a corporation is equivalent to forming it for the purposes of the SEC regulations.
c) Reside outside the U.S. The SEC definition of U.S. Person does not appear to include non-resident U.S citizens [2], unlike the IRS definition of United States Person [3].
[1] Code of Federal Regulations, section 17 ("Commodities and Securities Exchanges"), part 230.902 ("Definitions") subsection k ("U.S. Person") part (1)(vii)(b) (for "formed by a U.S. person [...]").
http://www.law.cornell.edu/cfr/text/17/230.902
[2] same, but part (1)(i) which says "Any natural person resident in the United States", but does not seem to include non-resident U.S. citizens.
[3] United States Code title 26 ("Internal Revenue Code") section 7701 ("Definitions") subsection 30 ("United States Person") part A (for "a citizen or resident of the United States").
http://www.law.cornell.edu/uscode/text/26/7701
I want to emphasize that I am not a lawyer or particularly knowledgeable about this topic. I am posting this mostly to elicit input from more experienced members. I have no intention of following any of these ideas without consulting with lawyers in the US and the other countries involved, and I think anyone who reads this message should be at least that cautious.