Personally, I don't think that "The distribution should be close to linear" should be a constraint. h5 and h6 are extremely rare on Wikipedia, so I don't think it's worth degrading distinguishability of the high level headers in order to give these headers a unique size. In your suggested header examples, the h2, h3, and h4 headers feel like they have nearly the same weight. As these are by far the most commonly used headers it seems like it would be important to make them more distinguishable. At the very least, I don't think we need to worry about giving h6 a unique size.
Topic on User talk:Aron Manning/Vector headings typography fix
Thank you for the feedback. I've removed the "linear" constraint, it was not a hard constraint, "should be close" had a lot of leeway. See for ex. Minerva, where I've had to adjust for Roboto Slab and Georgia.
The steps there are: -0.2em, -0.3em+bold, -0.1em, -0.05em, -0.05em.
Making h5,h6 both the same size (1em) can be considered. I almost went with this solution for Minerva. This should be demonstrated with real examples, but unfortunately I've found no way to find pages using h6.
To easily distinguish the smallest usual heading h4 from article content, a +0.2em difference between content and h4 is necessary, therefore squashing h5-h6 wouldn't help this case in my opinion.
Note that h2-h3 is a -0.3em step as it was originally. The difference you see is the same as on the live sites.
For h3-h4 I've made an adjustment to increase the step from 0.1em to 0.2em. The h2-h4 range can be increased by making h2,h3 bigger with +0.2em, not just +0.1em. The difference between h1-h2 is not important, as h1 - only used for the article title - is clearly distinguishable. This solution serves best all the conflicting targets.
Alternatively, the whole range can be extended by making h1 (and h2,h3) bigger. I personally prefer the size 2em used in Timeless, but assume there are many people who prefer the way it is now. That's only an assumption, though.
The range we work in is limited, so we have to make trade-offs, but there are many possible solutions. If you have any specific sizing in mind, feel free to share it.
Ping @Kaldari if you have any feedback about the solution adjusted to better distinguish h3-h4.