Comment by LegionMammal978

The diagrams shown might be possible with that restriction if we allow "Jenga-like" moves: first, create a single vertical stack with the full height. Then, to widen a row with an extra tile, push the row exactly half a tile length to the left, and slide the new tile into the gap. (Since the tiles are frictionless, this would be much easier than real Jenga!) At every point, the stack should be balanced, even if it is not stable. Continue widening individual rows until the final pattern has been generated.

Intuitively, it looks like there should be a valid sequence of row widenings that generates the "brick-wall" stacks, though I am not 100% certain. Assuming there is, the next question would be whether asymmetric patterns such as that "oil-lamp" stacks can be generated, or whether in general the optimal pattern can always be generated.