Apparantly, I was too optimistic in the comment to the first post about spam. Spam has continued to trickle in daily, although it does seem levels have come down.
It seems BBblog doesn't make it impoossible to enter comments when comments are turned off for a post, because I do see comments coming in for posts that have them turned off. They even usually don't require approval, which is actually quite odd.
What I think is going on is that BBlog makes the rather naive assumption that if the form isn't there, comments are not going to be submitted. Unfortunately, simply not displaying the post and not taking any further action is quite effective at stopping regular human users from posting, but not at all to stop automated spam robots; they will just send the POST request directly without going through the form. (Never mind if you don't understand this, it just means BBlog's way of disallowing comments would seem to be quite silly).
Anyway, I've come across a different blog software, WordPress, and that looks a lot more solid, so I might give that a try if I find a good converter.