Hm... looking back on it, I probably should have stated my case for why it's impossible to solve the whole thing on a planar surface in a completely different way, but it's too late now for me to care. I've stayed up long enough for one night. Maybe I'll get to it some other time if noone understands what I was trying to say. XD
The point I was trying to make is this: you'll always need to get somewhere that you can't because of the arrangement of Five-Crosses A through C, so you need to put the whole thing on a torus or something to get there.
