If I didn't miss something, it looks like your only water container will be the camelbak.
Fire to boil water also seems to be out of question.
So you really need MicroPur tablets (or equivalent)
I don't have any clue about the size of the soap dish you are talking about.
Could you add a few paper coffee filters , to filter the water you will put in the Camelbak ?
Or maybe a permanent coffee filter ?

OTOH, the water may be clear enough in that area to not need any filtering