So terrorists will continue to attack America whether they fit into the comfortable pigeon holes you prefer or not. You want to use the non-traditional nature of these enemies as a pretext to limit the President's powers to respond to them. They are warring with us, but it's not really a war, if I understand your meaning, therefore the President can't, or should not be able to, respond with the full authority of the Commander in Chief. But instead must, what? What sort of oversight do you have in mind? Surely you don't mean to say that the President can't do anything until Congress declares war? Also, do you mean to say that a terrorist who has attacked us before and who is known to be plotting to attack us again and is urging others to attack us is not at war with us and is not a fit target for military action? Is this the sort of creature that you would insist that the President must wait on a Congressional declaration of war to deal with?
This seems to me to be unworkable and unwieldy, and that it will be to our detriment to hamstring the President and thereby hamstring the military in this way.