Ok, for the moment, I have done the following:
1) All messages require moderation. I will undo this at some point, but for now, it seems prudent.
2) Any new members that want to join will have to request an invite. I've asked for them to prove they are human and not a spam-bot. :)
3) I have marked all the messages that are truly spam back since September as spam.
I wish there were an option for new members requiring approval before they can post, but the closest is that new members posts are moderated and at the moment, that's not good enough.
Hopefully this will get things under control. I'm on vacation (ish) from work now through the end of the year so I should be able to keep an eye on things.
Happy holidays,
kristin