There is no due process with the “terror” watch list, when they put aliases of terrorists and every permutation of a suspected terrorist on the list, and the innocent people with those names can’t figure out how to get off.
And there are public officials like Air Marshalls and a congressman who got off only to be put back on by some other process.
If due process is added then it should be doable.
Even if there were a statutory appeal process to get off of the list, it would be like appealing a federal agency determination that your stock tank is a protected wetland. Years and hundreds of thousands of dollars later, your grandkids may be able to buy a gun.