Your state level issue is largely handled by the Federal Preemption clause in Article VI, clause 2.
Hmm, you might want to reread that clause. it establishes the Constitution as the "supreme law of the land".
It does NOT say that a State can't do something that is specifically forbidden to Congress.
Now, the 14th Amendment DOES pretty much accomplish your objective. Of course, there were 75 years or so between the Constitution and the 14th Amendment, during which, by your logic the "much stronger" "Congress shall make no laws" could have been overridden by State laws. Or local laws.
Personally, I still find "shall not be infringed" to be stronger than "Congress shall make no law". But YMMV....