The best thing to do is:
Go to the back of Lazzaretto.
Wait for someone who knows where they're going.
Wave at em and point to the cut, then take off after them.
Or: Go at extreme low tide and idle speed in the middle of what's left of the cut. You'll have 1 to 3 ft of water throughout the cut.
And save your line on your gps.
DON'T!!! Go through at mid and ebbing tide by yourself for the 1st time, what looks like good water is really not!
Sorry, after rereading your question you're trying to get to the intercoastal. In that case from Lazzaretto, go out int the bay and go up the south channel, (if your vessel will go under pulaski bridge) then you'll t-bone into the intercoastal.
Right where south channel is about to run into intercoastal I run about 50 yards from starboard bank and trim up.
Dont be in the middle of the south channel when it meets the intercoastal cause it's just mud.
Good luck!