It has been a few months since I got Beats Audio working correctly, but I forgot to post about it.
As I told earlier I thought that deleting Beats Audio had solved the fluctuation problem, but one day I listened to the song 'Lilies' from Bat For Lashes, and at 1:10 there is a long synth sound that should have a constant volume level, but now it became louder and louder. Then I tested other songs and found out, that although deleting Beats Audio had made the problem less noticeable, it was still there on some songs.
I decided to try the solution by Andrew_S89 and downloaded Beats Audio yet again (sp57966.exe) and installed it. After that I tried 'Lilies' again and to my surprise the fluctuation was gone! I hadn't even played with the white EQ bands yet. At the moment I have Bass and Treble at 0, Center at 10 and Space and Focus at 30 and still the sound is smooth.
I had installed and unintalled Beats Audio few times before and it didn't have any effect, but now suddenly the problem was gone. I don't know if deleting Beats Audio helped or is it just sheer luck that I got the Beats Audio driver to install just correctly. I don't know. But the fluctuation is gone. So maybe you just have to try again and again (first delete Beats Audio the way I did) and maybe you also get rid of the problem. And maybe the HP experts have been right saying that the newest driver should solve the problem, but to get the driver installed correctly is the tricky part.