Ok technically I cheated on the last 2 cause I screwed it up in a rush, but you see what I mean. Finally thought I'd capture a video of my setup. Runs through a few different ways to set up the 3rd/4th TSTs from every set of 4 (it works in sets of 4).
Watching it now there were still a few bad placements and wasted t's but I still don't know whether to believe this setup is infinitely possible or not.