I'm in the middle of doing it myself and thought it might help others to post what I found.
I started on the blue teleport on the bottom left and cleared as I went. The teleports linked in series - 2 teleports in each 'room' - until I had placed the first plate piece. I then had to reuse the teleport to that room but it took me to a different room. So on I went until after placing the second piece I again had to reuse a teleport. This took me back to where I had come from and the trick here is to immediately go back into the teleport you arrived by. This gets you to a new area. Using the other one in the room gets you in a loop.
Placing piece three you go bck to a room you've been in before. Resue same tp to get to another room you've already visited. Reuse arrival tp again gets you to the room for pedestal 4. Reuse this tp and reuse again in the next room to get back to the main room with an unused tp in the lower right corner.
Using that tp I got to a new area. Clearing to the end and using the 2nd tp got me to a loop. I then resued the arrival tp and got to a new room. After that the crazy looping started!
Sorry this part is not more explicit, but I did eventually get to pedestal 5, and it was only 3 tps from there to pedestal 6.
I recommend clearing as you go to avoid having to try to revisit any areas later!