While I share your feeling that a valid carry concealed permit should be recognized in all fifty states same a driver’s license, I strongly recommend that you do not proceed with driving thru the states you mention while carrying. You risk dire consequences if you are caught and may likely even loose your CC license from your home state, as those state may report that you committed a crime with a firearm. In NJ you don’t even want to get caught with a hollow point bullet in the vehicle. I live in Pa, and carry concealed. One day while at a Home Depot in Pa I found they were out of what I wanted to purchase but they checked a Home Depot just across the river in NJ had in stock what I wanted. I am so used to carry conceal that I didn’t give a thought to it until in NJ. I was very conscious of my speed and turn signals until I got back to Pa.
Best wishes and safe travels