How can I 'share' lights between multiple circuits?
The problem is, whenever you turn one set of lights on, power can go through that shared light into the other circuit.  So each switch controls all lights.  While it -might- be possible to make 2 light groups (1 common light) work the way you want with two 4-way switches back-wired through each other, you're asking for something even more complicated.  Each switch interacts with 2 others, which means you'd need at least triple-circuit switches (likely paired 4-ways).  I don't think they make those.  Certainly not in home light switch form-factors.

This will be much easier if you start with home-automation tools.  Most vendors make an in-wall module for a slave device; then you just need to install and configure smart switches to manage them.  Or you could go for all wifi bulbs, and have the option of other light patterns if you wanted.  And maybe even programmable color.