End of the story...
Removing the auto-decomp didn't work for me. The bike wouldn't start no matter what.
So back to the old setup with auto-decomp on. Sure it's loud on idle but at least it works.
I cleaned up the camshaft, auto-decomp, oiled generously everything and assembled engine top for the last time. As soon as the top was on I started the engine hoping for a change. Nope... the engine greeted me with good, old click-clacking.
Oh well... I spent the rest of the afternoon assembling the bike all together.
Then I started the engine and... surprise! Clean sound with no clicking!
My personal bet is on dirty camshaft and auto-decomp. I guess the previous owner was not much concerned about oil changes so dirty residue build up and stoped auto-decomp from moving freely.