I create a shaded orange square whose height matched that of the column shafts.
I circumscribe a circle around it, and I notice that the intermediate column axes are halfway between the sides of the square and the vertical tangents to the circle. The span between those orange vertical axes is therefore 1.207 = (1 + root2)/2.
The same circle reaches up to height 1.207, at the base of the figural frieze in the entablature.
I also create an arc whose center is the centerpoint of the façade baseline, so that it sweeps through the upper corners of the shaded square. The top of this arc locates the top edge of the capitals. This geometry relates to the Golden Section (Phi), such that the top edge of the capitals lies Phi-1 = 1.618 -1 = 1.118 units above the baseline. In other words, the height of capitals is 11.8% as great as the height of the shafts. The big double square that you discovered in your analysis, similarly, is 11.8% bigger than the one I got from the pier axes.
I also infer from this structure that the inner column axes are supposed to be .500 units apart, and that the greater displacement of the right-hand one is a mistake. I carry those orange axes upward to the top of the composition.
To climb upward, I first draw 45-degree lines from the corner of the shaded square, so that they converge at height 1.500. The slope of the main pediment seems to have been set by connecting the vertex of the resulting triangle with the points at height 1.207 on the outer column axes.
The principal horizontal crease just above the pediment is at height 1.618, i.e. exactly the Goldne section of the first story’s column height. This height can be found by unfolding the half-diagonal of the shaded square, and the heavy orange arc indicates. This will be a big deal for later.
Meanwhile, I also note that the orange diagonals launched from the column axes at height 1.000 converge at height 1.802, locating the top of the main blocks in the statue bases. These lines continue upwards to meet the column axes at height 2.618, or 1+Phi, which locates the base of the second, broken, pediment.