It's downright quirky that I can get a visa to do it from Japan, a country which, ahem, has not historically been known for its welcoming embrace of foreigners. (Long story short: my previous employers know how the game is played, and keeping a status of residence once you have it is pretty trivial: pay taxes, file forms in a timely fashion, and don't get arrested.)
A green card is equivalent to Japanese permanent residence, which I don't have. (I would theoretically have been able to apply for it six months prior to leaving the day job, which would result in me getting it about a week prior to leaving the job, but the day job would have had to go to bat for me to get it and I thought telling them to go to bat then quitting would be discourteous. My odds of permanent residence prior to marrying a Japanese woman now are exactly equivalent to my odds of being featured on the front page of the Japanese economic newspaper, since any success in my business sufficient to justify one would justify the other.)
