Look, I understand you're trying to support your argument by drawing comparisons to another better-defined war, but your particular choice of wars is baffling. Most often, comparisons are made to the American civil war; Lincoln's explorations of executive power in the face of an existential threat to the republic are profoundly relevant to this debate. WW2... I'm at a loss.
The 2001 AUMF, for example, is as far removed from the US declaration of war against the axis as you can get. It's everything that a typical formal declaration of war isn't, with the vaguest possible definitions of who the enemy is and where the battle can be fought. It has no real limits of any kind, and has henceforth been used as a license for indefinite military action.
>"Nobody in al Qaeda wears a uniform; they deliberately avoid them, to maximize the probability that their opponents will kill innocent civilians."
I may be a bit slow, but honestly I already knew this :) Yes this conflict is very different from the canonical 20th century wars which naturally shape our views of what war "ought" to be. Our laws and treaties are inadequate, and leave us in troubling gray areas, and I'm not convinced there are any good ways out.
BUT...
I'm also pretty sure a good solution is NOT to simply give the president the license to do whatever he wants to whomever he labels a "terrorist", regardless of location or citizenship. This is precisely the license assumed by the Bush administration during John Yoo's tenure. It appears to be the basis of your own assertions as well; please tell me I'm wrong.