I hope this characterization doesn't inform the new commander's strategy.
The “nonmilitary solutions” is hopefully their way of phrasing Petraeus’ strategy of going town by town isolating the enemy, destroying them, and then controlling the cleansed area.
Part of that is his “hearts and minds” campaign of local presence by our troops. Obviously, if they go straight to the 2nd part without implementing the 1st part, it simply won’t work. The taliban don’t make nice.
Find the roaches, kill them, and then apply insecticide.
In this case, they need to block all supply routes. We know that they aren’t making their own weapons and ammo. How to stop it getting in. As mountainous as the east and south is, there have to be chokepoints to control resupply from that direction. The problem will be resupply from Iran.