I just gunna jump in here. Im not 100 % but i'm pretty sure that soaking with Epsom Salts works by creating a saline solution which fungus etc can not inhabit.
However from my understanding its quite critical to have an exact measurement (from google) of one cup of water to ½ teaspoon of salt . ( Epsom Salt my be stronger than normal salt in this respect i'm nt sure)
for the body/lips to properly absorb/ not reject the Epsom Salt soak i think its very important to hit this level of salt dilution.
Hope this help, if i can find where i read all this suff i will post but i think it might have even been on the original Epsom Salt post.