Well, first off, the fact that the right to arms does not in any manner depend on the words of the 2nd for its existence dispenses with your "interpretation".
In addition, you (and Justice Stevens) are wrong on militia law.
There is no claimable right for citizens to join a militia or to form a militia.
Militias can only be formed under the authority of Art I, § 8, cl's 15 & 16.
Presser v Illinois was very clear on the "rights" of citizens as it relates to militia.
"The right voluntarily to associate together as a military company or organization, or to drill or parade with arms, without, and independent of, an act of congress or law of the state authorizing the same, is not an attribute of national citizenship. Military organization and military drill and parade under arms are subjects especially under the control of the government of every country. They cannot be claimed as a right independent of law. Under our political system they are subject to the regulation and control of the state and federal governments, acting in due regard to their respective prerogatives and powers. The constitution and laws of the United States will be searched in vain for any support to the view that these rights are privileges and immunities of citizens of the United States independent of some specific legislation on the subject."
PRESSER v. STATE OF ILLINOIS, 116 U.S. 252, (1886)
Sorry, wrong again. It just doesn't work that way.
SCOTUS has said that the very purpose of the Bill of Rights was to withdraw certain subjects from the vicissitudes of political controversy, to place them beyond the reach of majorities and officials and to establish them as permanent legal principles to be applied by the courts. Even further, "the right of the people to keep and bear arms" is held among the fundamental, individual rights whose nature demands that they may not be submitted to any vote nor do they depend on the outcome of any election.
.