Anyone who may be interested will find the score to GOLDEN APPLE on archive.org. For some reason, it appears to have fallen out of copyright — if archive.org puts it up, you know it's been vetted.
I'm surprised no one's mentioned PRETTYBELLE, the vehicle written for Angela Lansbury after MAME. "When I'm Drunk, I'm Beautiful" is such a wonderfully demented song, and this is a show that is so un-PC it would make MORMON look positively tame. Perhaps it's time for a revival?
And I dont know that they would be considered "quirky", but I've been looking at old shows that, while wild successes in their time, are now utterly forgotten. THE GEISHA. THE PNK LADY (which has one of the most gorgeous scores ever written, by Ivan Carryl, who was something of the Sondheim of the turn of the last century — you can find a lot of his stuff at archive.org as well). MR. POPPINS OF IGGLINGTON. Granted, it was the books that killed a lot of these, but in some cases, like PINK LADY, the script is still incredibly solid.
http://docandraider.com