I think a reply button to antipoint contributions would be a good idea. It would retain anonymity, but allow users to reply to certain messages left to them with pos or neg antipoints. An example being:

"That's a good though!" Notice, no sig, so you can't say thanks or ask them what exactly they thought was a good thought. You just have to go back to the URL of the original post, and ask who it was that gave the antipoints and ask them why they did it. Also, if someone gave you positive antipoints without a sig, and you'd like to just say thank you or something, and ask for their contribution to your thought, you could reply and ask for their nick so you guys could have a pm conversation on the subject. Anyone like this idea? I could elaborate 100 times more than I have, but like my mood thing says, I gotta help get ready for my brother's birthday party today. Thanks!