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Don, Shinnecock can be a killer--literally. You very definitely want to enter during slack current in daylight, probably slack after high water because there is frequent and changing shoaling inside, proceed with due caution and check with USCG Shinnecock before you enter to get any updates. Remember the fishing fleet, such as it is, is also going to be transiting at slack and they'll often need some room.
Stakes, more than channel marks, are likely to be your best guide to where the water is passable. Either way--you want the chart, updated.
From the charts it looks like both bays (Tiana and Shinnecock) are designated fish trap areas anyplace they'd be deep enough for you to get out of the channel, good luck on finding an anchorage. I can't say I've ever been tempted to take a sailboat in there.
If no one else has answers for you--try calling USCG Shinnecock. Sometimes they answer the phone, sometimes they'll even say something besides "We're not allowed to talk about that." (Honest, at one time they wouldn't even confirm slack current times "due to liability issues".)