As a mod on two other SE sites and a long-time creator and moderator of online communities, I feel for you.
May I share some principles to help guide your considerations?
Abusers want attention, even if it's extremely negative. Deny them this and they will go away.
Time is of the essence. Online communities are inherently fragile, even when closely moderated. Continue to be fair but take action quickly and do not hesitate to be firm.
A transparent public policy is your best tool. When your FAQ or a prominent meta thread says "this kind of behavior will get the following response from the community," you can carry out your action with minimal numbers of complaints, flags, comments, and meta threads.
These principles suggest some elements to consider in your solution:
Principle 1 supports those who call for deleting all affected questions. If you wish to ameliorate the effect, you can permanently suspend all accounts known to be sockpuppets. There is no reason for those suspensions ever to expire. In the meantime, their questions will stand and answerers will retain their reputation points.
This principle also suggests minimizing comments and meta threads dealing with the abuser. Moderators should consider deleting all such discussions. Make the abuser's mark on the site disappear!
Principle 2 indicates the time has passed to give second chances or warnings. Act unilaterally.
Principle 3 is often carried out in the breach by posting previously unwritten rules or policies when they are found to be broken. This helps in the future and it keeps the moderators (and the entire community) consistent. (Abusers love to find and flout apparent inconsistencies.)
One noteworthy personal experience concerns a problematic individual on one of my sites who was attacking me personally. Let's call him "Harry." As a mod I was willing to put up with it, in retrospect for too long. Eventually I consulted other mods on Teachers' Lounge, a SE chat room dedicated to moderation. The moment I named this individual, mods from three other SE sites piped up to say "Oh, do you mean that Harry! Guess what problems he caused for us!" And laughter all around... . The moral of this story is that consulting early in the process with other moderators can reveal unexpected information and garner helpful advice. It can also show that you're not alone.