Wow, that's a lot of work and uses a fair amount of energy (heating the soap, hot water for washing the pot, etc.).
When the soap gets down to a sliver but before it's small enough to break, get a new bar of soap and just do the Vulcan soap-meld by holding the sliver onto the new bar and use. After a few wetting/drying cycles the sliver will be one with the new bar.
Yes, there is a lot of energy used in the process. I did it the first time only to see if it could be done. I have already acknowledged that using a net bag is the thing to do. ;-)