GENERAL IDEA:

Convert a 5-bit base 2 number into a 2-digit base 6 number. 0 is fire, 1 is salt (this is the opposite of what you might expect), and the metals are however many quicksilver you need to promote lead into that metal (lead is 0, gold is 5).

THING I DON'T WANT TO DO:

Division. Parsing a 31-atom-long stick of quicksilver sounds lame and hard.

THING I CAN DO INSTEAD:

Divide as I go along. Imagine a magical two-atom metal molecule where if you try to project the right side when it's already gold, it resets to lead and the left side projects instead. Instead of dumping tons of quicksilver into the right side, sometimes we'll know the bit is greater than 6 in advance. So, for the bit representing 8, we don't project the right side 8 times; we project the left side once and the right side twice. I do this with both the 16 and the 8 in order to do less division.

DIGIT TWIDDLING:

Also we can interpret the 16 as an 18. That still works! We'll end up with numbers from 0 to 33, but skip 16 and 17. That still fits in the 36 possibilities and in metal representation.

CARRY MATH:

With that trick, the magical right atom only ever gets projected 9 times at most. If I order the bits in a way most convenient to me, it will be projected up to 5 times for most of the bits, and then the last 4 times at the final bit. The final bit is interesting because if it's 0, I guaranteed do not have to do a carry operation, which I exploit for conditionals.

UN-MAGIC-ING THE MAGIC:

I prepare a 3-atom lead tringle. One of the leads will be the upper digit, but we don't know in advance which of the other leads will be the lower digit--I call them the lower digit and the bleedover digit. There is a hare-brained conditional purification scheme on one of the leads where I try to soak up all of the quicksilver using both leads, prioritizing the lower digit, and everything else goes into the bleedover. The last quicksilver only goes to the lower digit. If the lower digit is already full, then I can grab that quicksilver and do zany conditionals to output the two atom pair of upper+bleedover, but also project the upper by one more, and that's a carry operation. If the lower digit isn't full, then that conditional outputs upper+lower instead. Either way, we get a waste atom. Peep the chain.

RATE NOTES:

Up to 13 quicksilver may be used in this design, and the conditionals can operate at pseudo-period 3 at best, limiting this design's rate to 39. My actual rate is 42; one of the hexarms needs to stop to do the carry conditional.