I realize that the un-paid side of the forums are probably not funded for minute-by-minute moderation activity, but unfortunately I think that that may be necessary until the spam issue is locked down.
Does the new forum software support the "new posters require moderation until marked otherwise" feature that some forums have? (I don't actually know what it's called.) If so, that could be an option to keep the forums clear without minute-by-minute moderator activity--mark the preexisting posters as not needing moderation, and new accounts wait a day or two for their posts to flow through.
Edited to add: I'm concerned that perhaps there is no one who is authorized to delete posts and ban accounts? The primary spammer has been at it for several hours, some of them I believe business hours. I'd have expected him to be banned by now.
Again, I realize that I'm not paying anything for my use of the forum, so I have no grounds to gripe. But this seems likely to damage the reputation of the site as a whole.