Well, I'm vague because I don't have specifics to your install and every single thing you tried.
Obviously, with that many getting in, something is wrong somewhere. it could be many things and I don't have the info on what you do have running and what settings you have everywhere nor the information in your access logs.
what's the link to your site, for starters?
Do you have a separate bbpress install integrated? If so, did you disable signups in that?
Did you look at access logs and cross-reference them with the registration logs?
I've been blocking IPs. There are thousands of IPs hitting me. literally.
Have you banned whole ranges? Yes, it's drastic, but if most of them are coming from, for example, Chinese IPs and your site in English, then ban the IP at a higer level.
ban 123.456.*.* instead of 123.456.789.012
It's also quite possible you're on a host where the bots crawl the box endlessly. (long shot, but still applies)
There's not much you can do on the WordPess side, as the buddypress registration completely takes over the WordPress one.
Having said that - have you renamed wp-signup.php to a .txt file?
You have to narrow down how they are getting to your site first. Otherwise, we're just tossing guesses around.
Again, I can't exactly say "here's this one thing, go do it" because there isn't just one thing. I have a list of things to check; that's it. That's all any of us do. I can say I have my own sites running with open signups and don't have the same issue.
I have no idea where your site even is. You're asking me to help blind.
And finally - it is also quite possible that whatever version of BP you are on is just broken. will it be sorted in the next version? Possibly. But it's 100% a buddypress issues and the thread should be dealt with over in their forum. I can't even point you to old threads on their forums where I *know* we dealt with every single method, because the search on the BP site is broken.