Agonisingly close to 18R - It works if arm 14 can move the final vitae one cycle earlier. However, that swing collides with the output rotation :(

Conduits limit to input every 3 on whichever input atom needs to use both conduits. As such, I believe theoretical min cycles is 119C @ N=36*3 + L=12 -1. (Debond, Calcify, Anime (x3), Conduit twice (x6), Bond) 

However in practice, I'm reasonably sure that you need at least 3 actions to take the final vitae to the final bond, and calcifying one but not the other fire before conduit is too impractical. This put practical min and thus my target at 122C.