I was thinking about your project. I've done a little braiding, and found this "Easy Braiding Soap Recipe" I thought you might be interested in. It came from Australian Plaiters and Whipmakers Association website (which may no longer exist).
You will need:
A pot, a spoon, and your stove
A cheese grater
One (standard size) 4.5oz bar of pure Ivory soap
One and a half cups of water
One pound of lard
A sturdy container with a lid that seals (to store your braiding soap in after you’ve made it)
1. Grate the bar of soap into the pot with the water slowly, over medium to medium low heat, while stirring often. Bring the water to a low boil then back down again several times while stirring in order to dissolve the soap as completely as possible into the water.
2. Add the lard and stir it in until it is creamy and there are no lumps left. Be careful at this step to not let the solution boil.
3. Carefully pour the mixture into your storage container. Continue stirring your plaiting soap about once every half hour until it starts to cool enough that it becomes difficult to stir. Then seal the lid on, and wait overnight for the mixture to become firm. When you are not using your braiding soap, always keep the lid on.