I have never tried this on a stock or anything close, but I took a few foods classes back in the day and the trick to taking salt out of a stew or soup is to add a whole peeled potatoe to it. Maybe adding one to your fresh water soak will yield some results. I have used this trick many times, but as i said i have never used it for anything close to your needs. If you do try it please let me know how you make out.
Abraham Lincoln made all men free, Samuel Colt made them equal.