1. "This isn't welcome here." Should be flagged instead, and often is.
2. "This is factually incorrect but I won't comment as to why." I view this as lazy at best, and giving cover to #3 at worst.
3. "I disagree with this." Frankly this is the worst use of the downvote. If you disagree, say why (respectfully)!
Tags in Stack Overflow are pretty common (while they're not here) so I'd expect this approach to work better over there (first).
Downvoting to show disagreement is endorsed by the primary directing mind of HN (pg).
I agree that I'd like to see disagreement and quality indicators separated. Personally I like the Slashdot voting system: multiple dimensions with meta-moderation, and ability to boost certain types of material so you see more of it (so for example if you're really anti-humour then you can hide it all by giving comments ranked as humorous a large negative "bonus" in your personal scheme).
This issue you raise is one I, and others, raised several times and basically got told "the owners like it that way, put up and shut up".
I think I saw this done on TripleByte's website during the sign-up process where they filter applications outside of the US (and a few other criteria) with an explanation and a promise that they were trying to fix this.
That form of UI is unusual but very friendly.
I think such a system could work for stackoverflow too: provide reasons like [off-topic, hostile, spam, ...], but don't provide others ([stupid-question, too-easy, ...]).
[1]: https://lobste.rs/about#downvotes