there are few (somewhat over used, but still good) arguments against your played out points.
one, the 2nd amendment is not just about militias. The case in Washington DC a month or so ago concluded that the 2nd amendment wording "the right of the people" is not referring to the people in the militia but to all citizens.
second, the phrasing in the amendment - while poorly worded - does not say that the purpose of the amendment is solely for the sake of a militia.
A well-regulated Militia, being necessary for the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.'
It would be a bit more obvious if there was a colon after the word 'State' but the point is that while the two phrase are related, the latter is not dependent on the first part.
if it instead read "A well-schooled electorate, being necessary to the security of a free State, the right of the people to keep and read Books, shall not be infringed" the meaning would be: since it is important for people to be educated when they vote and because voting is the most important part of our representative government, people have the right to keep and read books. Clearly voting is the motivation for the right to read but it is obviously not the only reason why people should be allowed to own books.