Well Mike, I guess I'll jump in with my two cents. I think your idea is fine but I would suggest you 1) put a screen filter in-line to the box and 2) ensure an easy way to fully open and have access to the box for cleaning. It's amazing how much soap scum, hair, etc. gets into my shower sump. While living aboard it needs cleaning about every two months if not sooner. I do like your idea of a diaphragm pump, my prefab sump has a float switch and impeller pump. It's mounted on a shelf in the bilge sump and it also is plumbed for overboard discharge.
My head sink drains both are plumbed to feed unto the toilets via rubber hoses which run under the toilet seats. Strange set up which I think was a result of the boat being on the great lakes for some of its life. One advantage is that the heads get flushed with fresh water frequently, otherwise i don't see much advantage in coastal areas.
Good luck with your project,
Don