After fighting with a problem for 10 months, I finally gave up and reinstalled the system today (but it took me 5 hours and I'm back to exactly the point I have been earlier today with the same - but unlocked - system; more on that below)
Yesterday, as a lot of people here, I set up a call with Apple support to maybe get a hint or two from them how do I approach the problem. I didn't expect much, and eventually the talk went more or less they way I expected. They completely don't know how to approach the problem. I even got an answer why - apparently they don't have any procedures or help protocols for the situation of half encrypted disk. I guess Apple really tries to avoid the problem, since even their own help line wasn't given any guidelines how to help people with this issue. My guess is it doesn't look good when you market your electronics with safety in mind, and then simple bug compromises this and breaks the integrity of that system. But anyways, the guy on the line was kind enough to admit he won't be able to help me too much, and so we ended the call with nice goodbyes.
So, todays release of El Capitan only pushed me to finally do something about it, and I decided to solve the issue for good which is so far only achievable by reinstalling the system. I was super worried about my data (almost one terabyte of important work things), and I wasn't sure enough, that if I do Time Machine back up of half encrypted files they will be ok.
So to clear things up for everyone - the moment you back up even full encrypted drive onto Time Machine, the mac decrypts it. You have to choose separate encryption for it in Time Machine settings.
I double checked it. I borrowed a drive from a friend, and set up a new backup. After 3-4 hours the drive was ready. I plugged it onto my sisters mac and started browsing every single file to see if they are ok. They were. I swept every weird corner of that disk (my files) and everything was working.
So to give you a quick guide of how I did it and what steps you need to pay attention to:
1. Get a drive, set up new Time Machine, and do a full backup of your disk
2. If you are panicking, make two of them ^^
3. Restart your mac, and after the chime press Command + R to enter Recovery Mode
4. Go into Disk Utility
5. Find your drive and unlock it by providing your password
6. Go to Erase tab
7. Important: Type a name of a partition that will be set up. This might be important if you have path-dependent aps or libraries (like my audio samples). You want to have the same drive name, and same paths for newly installed system
8. Important: In the format section, make sure you pick Mac OS Extended (Journaled). Don't pick the (..., Encrypted) version!
9. Erase the disk (for me it lasted a few seconds)
10. Quit Disk Utility
11. Find and click Reinstall OS X
12. Follow instructions on the screen.
13. After the system downloads/installs you will get into configuration manager
14. Important: This will be the first time OS will ask you if you want to turn on FileVault. Make sure you uncheck this box.
15. Important: At one point, there will be option to copy a data on your newly set up Mac from Time Machine backup or another Mac. Do it. Select that you want to copy everything (three checkboxes)
16. After everything is copied, you will have another configuration screen.
17. Important: You will be asked for the second time if you want to turn FileVault on. Again, uncheck the box.
After that, your OS will welcome you just as you left him before backups, only decrypted. 🙂
I managed to install El Capitan after that without any problems. Before, the installation app wouldn't let me through because of not finished encryption process.