I hope I fixed the situation.
I installed a forum mod that checks all new registrations against the
Stop Forum Spam database. This should prevent (most) new bots from registering.
Next, I decided to test all current members against the database. After some sanity checks to make sure there were no false positives, out of the 3958 members on this forum, 1487 (38%) came up as spammers based on their IP and/or e-mail address. 1416 of them have registered since June 2011.
I have deleted all 1487.
In the process I created a nice diagram that shows the member registrations per month on the forum:

So, I hope this solves it once and for all. And I hope future spam posts become an isolated incident.