Well, at least for the moment, as far as I can tell, all the spam is gone. Of course, the hours I spent deleting the spam are gone, too.
Thanks for your help, Soul Thief. And HomieBear is now an administrator.
I assume the people posting all these spam messages are poor people in India, who are paid a cent or a fraction of a cent for every spam they post. They seem to be individuals, rather than bots. As soon as I block them under one name, they come back under another name. They seem to post from 0 to 12 posts, mostly identical, before changing names. I'm not sure why they post in so many different threads, but I guess they get paid something for each thread and then something for each post in that thread. I wish I understood better how it works.
There are several things that would be a big help. If I could delete all the posts by a given user, or remove a user from membership instead of just blocking that user from posting, or if I could delete a thread instead of only being able to delete by topic. Or if I could block all messages containing a particular up address.
When I look up the up address of the spam poster, I'm told they are posting from my up address. Don't know how the do that.
Anyway, thanks again for the help.