Certainly, state gun laws are only restricted by their state constitution, correct?
No, state law cannot prempt Constitutional rights. The 14th amendment applied the bill of rights to the states. This is why exactly what is protected is so important and the nature of the right (individual or collective) matters.
If the right is individual and if the right extends absolutely to arms suitable to the militia (as says US v Miller, the last Supreme Court case to discuss the issue), then the states have no authority except raw power, to prohibit such weapons. If the right is collective to the states, then they can do about whatever they want.
The problem is, there is no Collective right that goes back to the founders. it only goes back to state law based on state Constitutions beginning in 1840. In fact, all this state law begins by stating specifically that the second does not apply to the states but only to the feds. The 14th eliminated this caveat.
Sure just like state laws that restrict freedom of speech and the press. Those are not covered by the first amendment...right? Oh wait the first amendment says "Congress shall make no law", the second does not. Further the 14th amendment states "No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States". The privileges and immunities in question were pretty much universally understood to be, at minimum, those protected by the first 8 amendments to the federal Constitution. (A right properly understood, is an immunity from governmental action)