See my edit to post # 14. To expand on it...
In order to do logistical miracles, supplies have to exist, or there must be access to the supplies necessary to produce the item you're seeking to produce. The best logistician in the world can't produce the ingredients of gunpowder out of thin air. Niter is the big issue. The Confederacy had access to niter from Britain through most of the war, and imported hundreds of thousands of pounds of it. That, rather than Confederate production, actually fueled most of the gunpowder production in the Confederacy. The Union won't have that access, because Britain controls almost the entire supply of niter which can be purchased overseas, and the Union is at war with Britain (and there is an effective British blockade in place to prevent importing from anybody else). The niter caves which the South mined during the war don't exist in the North (the bats which produce the niter don't like the cold temperatures). Yes, they can start collecting urine and excrement and setting up niter beds like the South did. But niter beds take 1-2 years to mature and start producing any niter. So, assuming the Trent War gets started in late 1861 or early 1862, you're looking at sometime in late 1863 before you'll see any niter out of those beds. And if you're going to produce the quantities you're going to need, you'll have to start diverting into the niter beds a good portion of the animal dung which is the main source of fertilizer in those days. So your agricultural production will start dropping as a result. Now you've got to deal with the possibility of starvation on top of the powder supply problem.