The battle your fighting can be won, but it will be costly and labor intensive. While running soft water in a tub is a no-no and could possibly void your warranty, you can increase the hardness to make it suitable. If it's as bad as you say it is I'd drain it, clean it, hose it down, vac it out, refill it through your water softener system and add calcium increaser to achieve the recommended hardness according to your manual or test strips. Depending on size it could require 1 entire bottle each time you fill it. But even then, at around $10 per bottle, I'm sure it's less costly than all the other products you'll be pouring into your water to remedy your current problems. Test any cleaners on the back side of the pillow first, if it's too caustic you don't want to have to stare at a melted divot in the foam. Good luck.