A belt sander or large orbital sander with a coarse grit would grind the texture away fairly quickly. It'll be messy, but it's necessary. The key is to not grind through the drywall's paper face. You just want to knock the largest of the bumps off so you can then skim it flat. Use light pressure and keep moving. Stop when you see the remaining voids in the texture diminishing to just a few.
I don't normally advocate sanding interior walls, but this might be the exception. An overlay is at least as much work and causes other problems. A skim coat by an amateur is unlikely to result in a flat finish.
Use eye, ear, and breathing protection.