Choice of Input:
1. We need to go fast, so use all 3 atoms available to us.
2. The math of 1 Vitae + 2 Saltlikes thankfully works out to a nice 3 inputs per output.
3. Looking at how the last inputs can be used to form the output, it becomes clear we need to minimize the things we need to do with the center air atoms - meaning the input should have bonds we can reuse for the output. This leaves us with three possible shapes, all with an air atom in the center: 60° bend, 120° bend and straight. 120° seems inconvenient as we'd need to fill in vitae closer to the center instead of at the outside. 60° is annoying to disassemble because it can't be slid off the input - so straight it is (the others probably still work but I haven't tried).

Solution:
1. Last output should meet penultimate output at 180°, so swing it once and the penultimate one twice the other way.
2. Having air in the center makes creating vitae kinda slow, meaning I need to prebuild a bit. Most of the solution needs to be able to run at period four instead of six because with the prebuilding it needs to speed up towards the end.
3. Optimizing this for cost? No thank you I'm happy to have a solve.