I think "being necessary to the security of a free state" is parenthetical either way, so the meaning should be no different.
For the most part, I agree.
Consider the following:
A well regulated Internet being necessary to the security of a free state, the right of the people to keep and bear Modems shall not be infringed.
Or
A well regulated universe being necessary for the sun to rise each morning, the right of the people to keep and bear arms, shall not be infringed.
Or
A well regulated carpenter being necessary to the security of a free state, the right of the people to keep and bear hammers shall not be infringed.
The Second Amendment clearly indicates that in order for a State to be able to raise a militia the government must not interfere with the individual citizen’s inherent right to gun ownership. Which State supports the notion of raising a well-regulated militia made up of their unarmed citizens? Remember, a single armed individual can be a militia