I have done that stretch as recently as 3 years ago. It is fraught with shoals (1 ft) narrow channels (20ft) and shifting markers. It was an unpleasent trip for us and I will never do it again. Some shoals are in the channnel between to markers. I have a k/c with 4'6" and 8' draft.
I used to sail the stretch from Barnegat to AC yeears ago when I kept my Islander 28 on Barnegat Bay as was very suprised how much it had deteriorated and was virtually impassable now to a keel boat.
We also had use Little Egg Harbor inlet back then, but I also agree with Tempest it is a shoaled inlet where the CG moves ball bouys ( very hard to see in the afternoon breeze and breakers) continously weekly due to the shifting shoals. I have seen a big Viking (the factory is across Great Bay and up the Mullica River) hit hard ad run aground in the inlet a few times when they are taking them out for their sea trials.
I would stay put in AC until you get the right conditions. We have used Kammermans there if you want to be connected to land in Clam Creek and dont want to pay for the Farley Marinas 5 bucks a foot. You can also anchor
across the channel from Clam Creek, but the current does roar through there.