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"It is obvious that the Founding Fathers couldn't even fathom the idea of going to war against an enemy who attacked America without Congress making a formal war declaration. "

The Founders were inspired (and hard workers). Here is all of Madison's notes on the debate:

"The Debates in the Federal Convention of 1787
reported by James Madison : August 17
Mr. BUTLER. The objections agst. the Legislature lie in [FN26] great degree agst. the Senate. He was for vesting the power in the President, who will have all the requisite qualities, and will not make war but when the Nation will support it.
Mr. MADISON and Mr. GERRY moved to insert "declare," striking out "make" war; leaving to the Executive the power to repel sudden attacks.
Mr. SHARMAN thought it stood very well. The Executive shd. be able to repel and not to commence war. "Make" [FN27] better than "declare" the latter narrowing the power too much.
Mr. GERRY never expected to hear in a republic a motion to empower the Executive alone to declare war.
Mr. ELSWORTH. there is a material difference between the cases of making war and making peace. It shd. be more easy to get out of war, than into it. War also is a simple and overt declaration. peace attended with intricate & secret negociations.
Mr. MASON was agst. giving the power of war to the Executive, because not safely to be trusted with it; or to the Senate, because not so constructed as to be entitled to it. He was for clogging rather than facilitating war; but for facilitating peace. He preferred "declare" to "make."
On the motion to insert declare-in place of make, it was agreed to. N. H. no. Mas. abst. Cont. no. [FN29] Pa. ay. Del. ay. Md."

Note he can definitely use war to repel (without any say by Congress), but not to commence, an attack.
Congress met seldom in those days and it took a long time to travel.

"Congress met seldom in those days and it took a long time to travel."

I think that you have just made a very significant point. One can readily accept the fact that in colonial times the ability of Congress to meet was limited and so the President naturally must have the power to act upon the exigencies of the moment to protect the country. But how in heaven's name can anyone accept Congress actually meeting and passing "resolutions" as a substitute for a delaration of war? I simply cannot accept this mode of operation in today's environment of "instant messaging."