This is not just posting an idea, this plugin actually exist I just don't know if the site can use it. I think this plugin could lay a really heavy punch on spammers, it definitely sounds hellish.
I don't know if this site is based on MyBB. The MyBB structured forums can use the MyBB plugins by default (if their versions matches the plugin.)
Links to the plugin:http://mods.mybb.com/view/hellban
Hellbanning is a simple concept: A hellbanned user's posts and threads are hidden from everyone but himself (and staff) making it seem that they are participating in the community normally but no one is responding to them. Once the user realizes that no one is responding to his posts and is giving him the silent treatment, he will most likely get frustrated and leave.
A notice is on all hellbanned user's posts and threads for staff to see that the user is hellbanned.
Use this and they won't realize they need to start another account to continue the spamming.