The first day I made a formula for computing the distance as a function of the length of the two sticks and made a 278.

With the week 1 stream I realized this might not be good enough. I re-did my formula now accounting for three different disassembly methods depending on what cycle the stick arrives mod 3, and several other details I had elided. I made a table of the best possible score for each pair of stick lengths, and found the maximum is 283; see the showcase.

(6, 10) is the only way to achieve a 282. Note the vitae-mors order is important.

In honor of maximum metric, solution title chosen to maximize hubris instead of minimize.