The dilemma you face stems from the ambiguous nature of the upvote button:
1. As an "agree" button - you upvote to get the perspective you share to be displayed more prominently to other people. It is a way for you to influence other readers.
2. As "it was useful to me and a good use of my time" button. You use it because you think other users will find it informative as well. In this case you are doing purely for the benefit of others.
3. As "it made me laugh or evoked some other emotions" button.
All three could be viewed as different dimensions of content and one item/comment can have different combinations along these dimensions.
It is complicated by the fact that content creators are actively optimizing their content along these dimensions to gain more visibility.
When I come to HN, as a reader, I want to see mostly informative content - which is only dimension 2. I don't want to be influenced or persuaded. And while I enjoy a good laugh - that's not my goal coming to HN. This makes the other two content dimensions contribute to noise.
Your suggestion to split out the upvote into separate labels like "agree", "informative" and "funny" [1] and to let users sort by the dimension of their choice may not solve the problem of separating "agree" from "informative" because there is no incentive for the voters to vote truthfully. People who upvote content they agree with want other people to see that content. If most users are sorting by informative then those voters will upvote content they agree with using the "informative" button.
I think you need to change the system of incentives in order for voters to upvote only informative content and not 1 and 3.
One way to do this is to make what you upvote have more consequences for the type of content you see in the future and less directly affect the ranking of that content for all users [2]. With a feedback loop like this the upvote button is no longer "what content do I want other people to see", but "what type of content do I want my future self to see". It makes you think before voting - "Was it worth my time?", "Is this kind of content aligned with my long term goals?"
[1] - Slashdot has something like this: "funny", "interesting", "insigthful" https://en.wikipedia.org/wiki/Slashdot#Peer_moderation but I don't think you can sort by it. Also, only a subset of users are given these moderator points.
[2] - I'm building https://linklonk.com that works this way.