It's possible to move any golem other than the diagonal ones around freely, without moving the diagonal ones out of alignment or making use of move order.
The most difficult part is getting a golem around a corner, so here's an illustration of that.
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Say you have golems at 1 and 2. Move Beethro to 3, only entering the inner ring from the diagonal.
Now those golems will be here:
Note that golem 1 is north of golem 2. This means you can be within five tiles of golem 1 while being six tiles away from golem 2, so golem 2 goes back to the decoy while golem 1 remains in place.
Now if Beethro goes to 3, Golem 1 moves southeast and Golem 2 remains diagonally aligned.
Similar techniques can be used to shuffle golems around near each edge without moving the diagonal golems. Basically, just make sure that if you need to get closer than the very edge of the box, you approach from a corner and don't get close enough to draw out a golem from another corner.
