I'm sorry, the Founding Fathers appear to disagree. If they meant the Letters of Marque to be an issue related to the Second Amendment, I imagine they would have either mentioned Letters of Marque in the 2A or they would have mentioned the 2A in the clause establishing the Letters of Marque. Being as neither is the case, they are clearly distinct issues, and this essay is focused strictly on the Second Amendment.
Private ownership of arms and 'terrible implements of war' came first. Private individuals designed, owned, possessed, and deployed these weapons. The founders relied on the individual citizens and groups of citizens to provide instruments of war and provided a means to commission their use. No restrictions mentioned.
The second amendment guarantees the right of the individual to keep and bear arms with no infringements.
The second amendment does not exist in isolation and cannot honestly be treated that way. It guarantees that the individual may keep and bear arms in the context of, but not restricted to contributing to the common defense.
Nothing in the second amenmendment (a modifier to the original document) restricts what arms a person may have. In fact, it specifically states that the RKBA may not be infringed.
We can disagree philosophically, but when you or anyone else begin to place legal restrictions on rights recognized and guaranteed by the Constitution, the we will go round and round.
Your 'common sense' says no unconvnetional weapons. The Kalifornia legislature's commons sense says no 'assault rifles', no small inexpensive concealable handguns, no sniper rifles, no high capacity magazines, etc. HCI's common sense says no handguns for citizens.
Either "shall not be infringed" means what it says or it doesn't. I say it does, you say it doesn't.