This is how private people lose the right to purchase chemicals and dynamite. :laughing:
Dig out the soil to the recommended depth to remove the offending plant roots, fill in with sand, and compact it. I'd also go a couple feet past the diameter of the pool just to have a buffer. Sand makes a good base for pavers, brick, etc... around the outside of the pool as well. You should put some sand under the area anyway to help protect the liner from roots and rocks.
I'd be skeptical about putting salt in the soil under the pool, as salt will attack your metal frame if it gets to it. Salt leaches. Once you put the pool over that area, it will draw moisture UP to the bottom of the liner, and out to the sides. That's right where your metal pool frame will be.
I have a salt water above ground pool. Everything is fine until you get a leak. If it's not detected and stopped, in a year or two, you can see corrosion and rust on the metal walls and frame, especially in areas where the paint is scratched. The most troublesome areas are where the skimmer and water return line go through the wall.