Energy, I have had a large Diadema urchin that I recently had to pull out of my system because it is now causing too much destruction to SPS pieces. However, it will eat GHA and bryopsis, and because of the way it hovers and lowers down to feed, it rarely knocked over anything in the tank. Only the stuff that was balanced precariously ended up falling over.
As it travelled the sand, it walks on its spines like little stilts, and would pick up this and that gently, pick it clean and lower it back down. It would travel over a patch of zoos and those didn't even bother closing up. It grew from a tiny little guy to a semi-decent monster.
When I got it (note the aiptasia to the right for a size comparison):
and now, surprisingly posing in front of the same zoos:
The shorter spined urchins are true bulldozers knocking over anything in their path, and the one I had loved coralline (the diadema does as well) and would chew a star pattern into the acrylic overflow. It was banished into my son's 29g and does no harm but that tank is LR, clownfish, and LTA and an eel.
Here it is:
I think you've gotten pretty good advice so far. If you have quite a bit of GHA now, it could be binding up the nitrate and phosphate giving you low readings, but manually picking it off (rinsing your hand each time to avoid releasing any into the system to land elsewhere is ideal) in a typical tank. In your tank, you need a fish or several fishes that eat it. Tangs and foxface are known to eat it.
Hope you can get it under control before it starts strangling some of your beautiful SPS pieces.