Maybe one should try to map out the whole C(GA) frontier, using many approaches that could all hit 31.  There are ways with batches of 3 (3rd at L=2) or 4 (2nd at L=2) in addition to this way with a batch of 6 and a catalyst.  I opted instead for something I hope resembles good intuition.  I brought mist of dousing to a very clean min with this approach, why not touchstone.

I did my best to enumerate all ways of incorporating both inputs at L=2, which was necessary to have for my approach even if not necessary in general.  I found that there was exactly one way, all others ran into conflict with the central 3 atoms needing overlapping glyphs.  Building around that one way, I found a finishing loop that ran at period 4, using 2 of each input, one extra fire per period, and a catalyst.  All of the demands were reasonable due to N=14.  So the final step was to get that material in place without ballooning the secondary, and eventually I settled on this.