I have suffered all my life with SD, and this may be in a similar vein in that salt has sodium and chloride, I have had considerable clearing using sodium hypochlorite otherwise known as bleach(Clorox). Healthy skin makes hypochlorous acid to kill off bacteria on the skin, and we all know SD skin is overrun with fungus and bacteria, especially malassezia. Adding a bit of acid to sodium hypochlorite creates hypochlorous acid.
So, I wash my skin and hair with 2% sodium hypochlorite(or Clorox diluted in water approx 1:3). You can also use Clorox straight. Then while the sodium hypochlorite is still on the skin and hair I pour a little vinegar into my hands and wipe it onto the skin and hair. Leave it on for a minute or two and rinse with water. No moisturizer. It will sting at first but that soon passes and then no longer stings at all.
For me, this has been very effective.
I use 2 chopped garlic cloves per day as internal bacterial control.
I found the sodium hypochlorite solution here in this pamphlet