My salad shooter with the grater wheel makes this so easy. Interesting about the KOH, I might try that next time. Mind you, I travel a lot and use my stuff for handwashing too, and never had any issue with dissolving, even when I (rarely) use cold water - like on a delicate cycle.
I totally find soap far better for laundry than any of the commercial detergents. Its cleaner and fresher for sure. I use 0% SF 100% CO and about 10% koh to help for a fast dissolving when in the washing machine, I add oxy bleach and washing soda always and all washing comes out bright, clean and fresh. The loathsome part is grating up the bars....sigh!!! I think I am going to get an electric cheese grater to do the job!