Ok so I've added a bounty to my own question and after a while I managed to fix it by myself.
Here's the question: Magento 1: unable to sort grid by custom attribute
Problem is Stackexchange tells me to assign the bounty to someone but the only answer different than mine is totally not helpful, has got negative score and it looks like the poster didn't read my question in details.
So I'm not sure about the action I should take in that case.