JoAnn, are the tall drumsticks the only ones that have been good perennials for you? I tried A. nigrum a few years ago, and they lasted 3 or 4 years, but nothing after that. I'm pretty sure it wasn't too much moisture for them (the drainage is good, and it's on a slope).
Deb, I've never planted any bulbous Alliums that reseeded, but your mention of the hair Allium reminded me of something I do find and pull out of the garden a lot, that sure don't look like any of the wildlings I've ever seen around here. I had wondered if my friend who lived in this house before me had planted some hair Allium. I don't find them attractive at all, and they've been a real pain.
