I've got the same problem in my creek especially during the winter which is our main crabbing time. The mouth of the canal has a bump of hard sand I have to cross. During times of hard NW winds, the water is blown out of the bay and I have to grind my way across the sand to get into the canal. A handful of times, I've had to leave the boat until the tide comes back in. I have a sacrificial piece of starboard screwed to the last six feet of keel to protect the fiberglass from wearing out. The boat is tough. We have actually laid her on her side a bit as we ground our way in or out.
If you have mud, you shouldn't have too much problem. Repeated trips will blow a path through the mud or you can just grind through it. I have had days where I had to sit it out until the blow is over and the tide returns. You aren't much different in NJ as we are in NY, one or two days of severe low tide and then the recovery begins and it's usually in the winter.