Aha...now I get it..
You should be able to remove the bladder and the pump (use it to dump your black water tank) and connect the sink drains to thru-hulls. Your galley sink should have no problem draining by gravity.However, I suspect from what you've said that the distance from the head sink to the galley sink thru-hull may be too far, or take too convoluted a route, to use the same thru-hull for both the galley and head sink drains. The simplest solution for that would be to use the same through-hull for head sink drain that the toilet intake uses..tee 'em together. This will also give you the ability to flush the sea water out of the sanitation system by closing the thru-hull, filling the sink and flushing the toilet. Glad you find the book useful!