Long time tournament stream enjoyer. This is my first ever serious attempt at a community puzzle. This solution was worked down from ~900i to 287i. I don't imagine reducing the period below 8 would help lower the instruction count. 

I set up a spreadsheet and found that purifying to 4x copper and 2x silver before projection uses 1 extra lead after output, while 5x copper and 1x silver produces 14 extra lead-equivelent. Doing 14x one process and 1x the other, then becomes a perfect ratio at 18+2/15r. With these numbers i could divine that psudo-period 16 was a good choice, and projecting onto all copper from tin and lead was a safe bet. The rest is conditionals to handle the excess quicksilver, produced at higher than 16r.

I really like how the motion of the output block pops quicksilver off the stack in the lower right.