Last time I looked home educated kids didn't do better on average when you corrected for parents. They even did worse than average in STEM fields, but of course since they were on average equal they did better on average on non-STEM subjects. This makes sense since it is mostly moms that home school and women are often weak at STEM themselves.
Your first link dares back to 1995 and a lot has changed since.
The data from Alaska is based on "students are enrolled in the state’s popular correspondence programs". If that implies state control of materials and syllabus it is more like school than real home education.
I think you are right in so far as there is a particular sizeable group (affluent hippie women in my experience in the UK) of home educators tend to encourage humanities and creative arts.
In general, the internet has been of huge help to home educators: online classes, better access to resources, online advice and community (only useful thing I have ever found on Facebook are HE groups!) so I would expect that to have had a major impact.
Can look at some links about this:
https://www.nheri.org/home-school-researcher-the-impact-of-h...
https://responsiblehomeschooling.org/the-homeschool-math-gap...