The first build was great, 1.1 will be AWEsome.
Can you slope the walls in a little bit as it rises? Maybe just the lowest course or two?
Then, if it settles, and if the middle bulges more than the bottom, it will only tilt itself to be straight up-and-down.
Or I wonder if it would help to give each level a few days to settle and stabilize before adding the weight of the next level. That way, if one level spread, you might still be able to tap those bricks back into place, if the weight above them was small enough.
I never thought of a multi-level spiral!
A multi-level wedding cake, maybe, but I'm not that ambitious.