This is a slight improvement over my original solve.

In theory, min cycles is 31. I started with the idea of shepherding one input through two bonding cycles and straight to the output, as you can see with arm 1. Unfortunately, the layout was a bit challenging to get a good period.

Originally I was going to use the leftover salt as the extra earth, and also figure out a second construction converting an earth-salt into an earth-fire instead of have the fire-salt converted to fire-earth every time. But then I realized that min cycles would actually require 4 different constructions, not 2, and I just never had the energy to go that far.