For the case where scores are used to measure agreement: a special kind of vote comment (like polls for submissions), to express agreement/disagreement.
A checkbox for whether you want your comment to be voted on, or evaluated. This is displayed, so HNers know how to treat it.
A "poll" comment doesn't count towards karma
I think your first suggestion touches an important point - it may be useful to consider the different reasons people vote on comments, which I believe are broadly:
a) they agree/disagree with the opinion stated in the comment
b) they accept/deny the factual accuracy of the comment
c) they feel the comment does/does not contribute to the overall discussion; in my experience here, this seems to be heavily influenced by a) and b)
and possibly
d) they like/dislike the person posting the comment
I find the scoring useful for cases b) and c); in case a) I've found the absence of scoring more useful as it gives me more space to think about my reaction to what's being said, and not just follow everyone else. Case d) is trickier - I don't think many people would agree to hiding account names as well but I think it would be an interesting exercise!
So, perhaps it would be helpful to categorise the voting a bit? Accurate/inaccurate, agree/disagree, contributes/doesn't? Of course, there is a usability trade-off.
A checkbox for whether you want your comment to be voted on, or evaluated. This is displayed, so HNers know how to treat it. A "poll" comment doesn't count towards karma