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I believe he meant "academic" in the sense of "having little practical relevance, a dry theoretical exercise." Composers who are exploring an idea, just so they can document what the extension of the idea looks like, and maybe write an article about the results, but without actually expecting great music to result. Kind of a scientific exploration of advanced music theory, rather than composing an actually piece. Like writing out an exercise from a harmony textbook. You may use what you learn to write something awesome later, but you don't expect the exercise itself to be great music.

The impression I get is that it is not "cool" to care about "how it sounds", at least in the academic/ avant-garde scene.

No, I mean people affiliated with the better universities or music institutes, people who participate in festivals like Darmstadt or Donaueschingen, and people who get written about in academic circles. People these days who focus on choir music or just intonation or even writing for conventional ensembles or using standard notation or whatever are generally considered to be behind the curve, or 'reactionary'

it's great to see exploration and experimentation - the only way to progress as a creative person is through pushing yourself out of your comfort zone, pushing your boundaries. These things should be relegated to rehearsals, open mic nights, or reading sessions. Having a group of musicians with whom to bounce/test ideas without fear or expectation was extremely liberating for me. The problem you're noting arises when a half-baked "concept" is passed off as a "composition" on a M.Mus Recital. And when people are too quick to give standing ovations and say "great work on that new piece", it only inflates the "academicness" of a vicious cycle... Just my thoughts on what I've come across too often, working in an improvisational setting, is that people who feel that "Further Out = Better" .

in context of a degree-progression, from what i know, all the intervals should be inverted/transposed to see whoever has the most valuable intervals in the whole progression. there are many things who contribute to making a central tone. not only if it has a fifth and a fourth, but in what order (the best case is where the tone is preceded by a fifth), who has the rhythmic accent (the first bar), which tone is the lowest in pitch in reality. after the central tone is established (which is hard sometimes) then all the chords reffer to this parent. this means that if there's a F chord going to the C chord, and C is the central tone, then the F is the forth, even if in reality it comes before the C chord, or if it's in a lower octave (lower F to higher C is has the interval of a fifth, but it doesn't matter), it's still considered 4-1 from a degree-progression's point of view. if F were the central tone, then it would be a 1 going to a fifth (1-5). the same notes on the staff. hope i got it right.

Since the third lends the quality to the chord (i.e. makes it major or minor) doubling the third can make it stand out more than you may want. Of course doubling the third is better than having parallel perfects, but you should avoid it if possible. They are only rules if you are a student or are doing a strict exercise. Otherwise all of it is just guidelines set forth for specific reasons. If it works in the musical context, you need not worry whether it is correct or not.

I think the rules differ according to the authority. CPE Bach says: "According to circumstances, the octave of the bass may be omitted and either the third of fifth doubled. However, when the third becomes major by chromatic alteration it is not played." I think this is a fairly liberal rule, as I understand it. It essentially only applies in minor keys or passages, and the rule follows from rules about treating leading tones. There is an additional "soft" rule that it is better to double roots or fifths, because otherwise it unbalances the chord from sounding like its function, but that rule is violated all the time in real music. Kirnberger has a similar rule to Bach. I'd have to do more research to see how the rule differs for others. What is the source for the rule as you understand it? Give a verbatim quote or screenshot.