Hi Jaan,
as you know I am not a guy spreading theories. And here is the biggest issue I can seen on the site:
Google have indexed 5120, and only 651 are in the main index, which means 4469 are in the supplemental results.
Once you fix that issue they will see a dramatic boost in their rankings.
I wrote an article about this, explaining your problem:
Boost your rankings with Pagerank Sculpting