I think I know what the mitigation is for anonymity aspect of the exploit. I will tell you I think it can be fixed going into the future, but we can't restore the anonymity from the past. It is fucked. Meaning if you thought you were anonymous you were not. The NSA can compute the intersections.
The best we could do (if I am correct) is to quickly checkpoint the code and get it out to 51% of the miners so we can prevent BCX's Time Warp attack. But fluffypony says we don't have to do anything rushed and he is at beach any way.
Then we put the mitigation in place so the future anonymity isn't broken.
However my mitigation proposal may still fail in the future when the attacker (NSA?) owns many inputs to many rings on the block chain. I haven't gotten that far in my very rushed analysis. So maybe I can devise a solution (but unlikely because I won't know which inputs the attacker owns) or it doesn't scale well for the attacker (our best hope but I am not optimistic).
So I would say yes ring signatures may be doomed, but I am not sure yet. Maybe not also. I hope not.
If only XMR was affected, there is one of my emotions that would love to see it destroyed. But on rational thought, I don't want to hurt the innocent parties who invested, some of whom are my friends (including but not just Rpietila).
So:
Checkpoint the block chain, periodically but unpredictably.
And:
Consider whether the ring signature NSA sybil issue you've contemplated is mitigated through Nash equilibrium effects? (Unraveling the privacy is complicated by multiple uncooperative entities attempting it, the more the merrier.) TOR has the same concern, though a less effective implementation due to resources.
Further consider the extent to which initiating such sybiling enriches mining efforts and further secures the coin.
The current plans for extending geographic diversity in userbase will also assist.