Another proposal: Visibility karma remains 1 to 1, and agreement karma acts as a weak multiplier when either positive or negative.
Could also give karma on that basis.
However thinking about it, I think the result would be people would start using the visibility vote to express opinion even more...
This is good for calibrating what the votes mean across the responses
A little ambiguous between "disagree karma & upvote karma should have equal weight" and "karma should have equal weight between people"
I think because the sorting is solely on karma, the line is "Everything above this is worth considering" / "Everything below this is not important" as opposed to "Everything above this is worth doing"
One situation I use strong votes for is whenever I do "upvote/disagree" or "downvote/agree". I do this to offset others who tend not to split their votes.
I think some kind of "strong vote income", perhaps just a daily limit as you say, would work.
Definitely, for example if people are bikeshedding (vigorously discussing something that doesn't matter very much)