A few thoughts on how to combat the spam:
1- Time-Limited hold on new users/accounts (1 week perhaps?), with a message apologizing for the hold and explaining why it's in place.
2- If you don't want to frustrate legitimate new users, give Mods the ability to delete spam comments/threads/accounts (this is assuming they don't already have this ability).
3- If there aren't enough Mods to handle the problem (just not enough of them in general, or aren't online frequently enough), perhaps ask for volunteers for a "Spam Squad", who would only have the ability to deal with spam.
Maybe put some requirements in place when accepting volunteers - must have been registered for X amount of time, must be online/active on the site frequently, etc.
If you don't want anyone other than Admin/Mods to have the ability to delete comments/threads/accounts, maybe give the Spam Squad the ability to "lock" an account and make comments/threads invisible until an Admin/Mod reviews it. This would halt the spammer and "clean up" the forums, and minimize any potential abuse (people deleting comments/threads/accounts that they shouldn't).