Ideas...
Jeff, you are right about the distilling plant, but I read that the plant only put out limited amounts and what came out was for batteries, cooking, and some hygenics among other things. I also read that the ship's cooks were the ONLY crew members aboard who were encouraged to shower daily to preserve water. The outside water usage seemed possibly logical...
As far as spinning vs. wringer, if you look at the top of the washer right under the wringer, you'll see a rectangular cover where the wringed out water could return to the washer to be reused, saving suds (there was NO room for a sink to save the suds water), water and room in the bilge that tub after tub would take up. I'm actually doing a little research to see if I can find how it worked, but you can almost make book that, at least as far as the enlisted men went, there were probably no individual loads, just community loads...
It also makes sense that there was no pump a nd it would gravity drain into the bilge. Too bad there was a wire door across the room opening. Probably put there to keep washer fanatics like me from tearing it apart to see how it ticked...
RCD