If you want it to still be textured, just not skin-removing-textured, could you knock the points off, then at that point see if you could either repaint OR messy-mud over it? I realize you now have parts that are completely non-textured, so it might not be an option, but I'm throwing it out there. I have a very heavy texture in my dining room and I LOVE it. I think you could achieve something similar to it using the above method.
This photo shows the texture the best, I think:
There are other sizes here...
I promise I painted the rest of the room after this!
Sorry so huge, I'll figure that out next.