I finally accepted that I was never going to take my bag to the laundromat, and all my neighbors have top-loading machines, too, so I decided to give hand-felting a try.
It worked out better than I expected, mostly because I expected a very long slog but it didn't take that long. Although, linking to the article now, I'm wishing I'd remembered the towel for cushioning the bucket. And I didn't bother with the tennis balls. And we broke our mesh colander at Thanksgiving, so I lined a plastic colander with cheesecloth instead.
I was pleasantly surprised by how nice the "poke hole with needle, push I-cord through" handles turned out, too.
Yay! All done!