I used to put a terry toweling washcloth in the centre of the unfolded inner and then roll both outer edges (which would be next to the legs once inside the outer wrap) into the centre. This makes 2 sausages of fabric with a trough between them. That helped to catch the poo and stop it running onto the seams of the wrap, and the washcloth made it all a bit more absorbant.

It doesn't always work, but i found rather than soaking each time i could leave the wraps lightly stained and every few weeks i would give them a good soak and wash and then hang them out on a sunny day. The sunlight bleaches them.

HTH