Sorry to hear about your troubles
I think you will be right to throw out the soap
if it has undissolved lye crystals in it. I don`t know if it is any point to rebatch it if you are not sure if you can get it to dissolve properly if you do, and it is a small batch, as you said.
And I don`t know for sure if your hard water could be the cause or at least contribute a great deal to the issue of the water, but it really doesn`t do you
any favours in this case either.
Can you get a hold of distilled water? Or demineralized water/de-ionized water? (the type you can use to refill the water in a car battery)
When I made the faux seawater I had no issues, the water was cloudy but no undisolved grains of salt or the bicarbonate. The lye dissolved just fine when I portioned out the part to use as my lye water. The rest of the quart I set asside in the fridge.