I was suggested to use bones instead of shape keys. I did some research, but Blender users are undecided over what is better and most seem to go with whatever works best on each specific situation. So I tried to use both. There's a lot of room for improvement, but I'll do better next time. I used bones for Libuše's individual lips and mouth corners, and shape keys for her brow, eyelids and cheeks. Behold the result.