In most of these particulars the power of the President will resemble equally that of the King of Great-Britain and the Governor of New-York. The most material points of difference are these--First; the President will have only the occasional command of such part of the militia of the nation, as by legislative provision may be called into the actual service of the Union. The King of Great-Britain and the Governor of New-York have at all times the entire command of the militia within their several jurisdictions. In this article therefore the power of the President would be inferior to that of either the Monarch or the Governor. Secondly; the President is to be Commander in Chief of the army and navy of the United States. In this respect his authority would be nominally the same with that of the King of Great-Britain, but in substance much inferior to it. It would amount to nothing more than the supreme command and direction of the military and naval forces, as first General and Admiral of the confederacy: while that of the British King extends to the declaring of war and to the raising and regulating of fleets and armies; all which by the Constitution under consideration would appertain to the Legislature.
The role of the President as Commander in Chief is to simply direct the armed forces after they have been called to action by the Congress of the United States. You are correct in the fact that the language in the Constitution is vague but I believe this to be the original intent.
To define and punish piracies and felonies committed on the high seas, and offenses against the law of nations; To declare war, grant letters of marque and reprisal, and make rules concerning captures on land and water;To raise and support armies, but no appropriation of money to that use shall be for a longer term than two years;
To provide and maintain a navy;
To make rules for the government and regulation of the land and naval forces;
To provide for calling forth the militia to execute the laws of the union, suppress insurrections and repel invasions;
So it appears to me that, as you point out, the Legislative Branch is vested with more military powers than the Executive, but I still do not see a requirement placed on the Legislature to declare war in order to call forth the militia. The power to call forth the militia is acceptable to repel invasions, with or without a declaration of war, based on a plain reading. Well then, nowadays we don't "call forth state militias", because we have a professional standing army, but the Legislature has authorized the calling forth of our Armed Forces, at the request of the Executive, for defensive purposes. Seems all right and proper to me.