Aqua Map has the Corps of Engineers (ACE) survey data available as a chart overlay, and it is very interesting -- not only for the narrow channel at South end but also a couple of substantial bars into the middle of the channel farther north. My takeaway is to look for tide that is at least (your draft) - 2.5 feet, and watch sonar (of course).
BTW the last time I went by there, we saw a beautiful 60 foot sailboat approaching the south entrance. The admiral commented on how they might have gone all over the world. I said I thought they were cutting the corner between the first 2 green buoys.
30 minutes later we heard a call on channel 16 that they were grounded. (And 2 hours later a call that they were underway again.)