I need a hint about how to get the balanced blocks to move one place to the left while still being balanced.
Correct about the right block to the left of the button. The way you are describing makes not much sense. In order to stack a block on top of another that is directional, you need something to hold it in place. The first stack should be above that block (leaning against the pillar) and the other stack should be to the left of the first stack .