Nothing especially fancy here. This checks all 12 times. With two checking stations that's 6 checks per output. On a match an atom is moved to the left side. Three matches allows the stick to wand the gold, which is then grabbed and wands away the salt.

Getting solves working was torture, especially finding berlo patterns that worked for both hexarms, but optimizing was quite fun, and I was finding saves every day right up to the deadline. This feels more like a proper sum solve than a weighted sum, and faster algorithms will likely trounce me.