Okay, so there's a few issues here that make this problem harder to tackle than simply using your suggestions of "just make a script that fixes it":

1. JCF runs on vBulletin, which is a product not made by the JCF staff, and hence is a lot harder to write any antispam script for than for Jazz2Online itself, which was completely coded by the J2O staff - not to mention that writing an actually effective antispam script is not all that easy.
2. We don't really have a lot of time.
3. Right now new registrations have to be approved manually before they can post on the forums. This fixes the problem of spambots on the forum themselves (as in, posting in threads and the like) but because of item 2 on this list, there is an absolutely gigantic backlog of users to be approved and genuine new users are caught in this backlog as well.
4. An alternative would be having new users PM an admin so they can then approve the user, so not all new users have to be checked manually. This would require us to allow unapproved users to send PMs (they are allowed to do so at the moment). That is however also the reason you're getting spam PMs in the first place. So there's no really easy solution out of this situation, except for writing a custom script, but see point 1 and 2 for why that's problematic as well.

There might be a vBulleting plugin that can help but this, but well... 2