Wow. That was indeed insane. Thanks SO MUCH to everyone who helped keep that under control. As a matter of fact, it was ALL gone when I arrived at the scene, with well over 500 reports in my email inbox! Well done gang!
Brief postmortem: There were 27 accounts, many of them registered with Outlook.* domains. I tried reporting the addresses to Outlook.com, but they weren’t at all interested in even trying to understand the issue. Shame on Microsoft and Outlook.com for their indifference.
From what I can tell, the accounts were probably manually created by hand, because there was enough variation in the quantity and style of the optionally filled-in information (“Location” field, avatar, etc.) to suggest that a human probably created the accounts. Then s/he proceeded to use an automated click tool to send a fire hose of spam. So I changed the CAPTCHA, and I don’t think it will happen again, at least not soon.
EDIT: Interestingly, another spam account and post just now appeared. It was using a VPN, so utterly impossible to block. And it was definitely a human user, because it read and understood the new CAPTCHA, and then navigated click-by-click through the forum structure to create the post instead of using a direct link to post.
Most of the accounts got automatically disabled thanks to your collective vigilance. But they probably would have been disabled even faster if the correct button had been consistently used. I noticed that a large number of times the Report button was used on these posts, which is not the correct way to handle spam. The Mark as SPAM button should always be used on clear cases of unknown (usually new) users posting obvious spam, not the Report button. You can read more about it here:
Again, thank you all VERY MUCH for your help, I really appreciate it!