With Japanese Prime Minister Yukio Hatoyama’s career now officially in the toilet (the sartorially challenged pol resigned yesterday), you’d think Vogue might nix its August editorial on the First Lady, Miyuki. Apparently not. Having already doled out big dollars to dispatch a cadre of staffers to Japan, along with Annie Leibovitz, to ready Hatoyama for its Age Issue, the mag will reportedly proceed with the spread. Like her husband, who recently donned a now infamous multi-color plaid shirt à la Jamie Foxx circa In Living Color, Hatoyama is already the object of a fair amount of ridicule in her home country. The onetime actress and author of 2008’s “Very Strange Things I’ve Encountered” claims to have been abducted by aliens, get energy boosts by “eating the sun,” and have met Tom Cruise in a past life. Sounds like a Vogue interview we’d actually read.