The simplest way to do this is to eliminate the sink drain seacock and diverter valve at the sink. There's no reason you can't drain the sink through the head intake seacock. If you want to flush the sink using fresh water from the head, just close the seacock. This is actually the method suggested by Peggie Hall, diva of marine heads and plumbing.
That said, what you've drawn is basically how my head sink is setup, excep there's no seacock on the sink drain, since it drains above the waterline, by about two feet, and there's little risk of heeling to submerse it on a trimaran.
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You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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Still—DON'T READ THAT POST AGAIN.