Nowhere in this document does it say that the entire region where ash clouds MIGHT occur should be closed to traffic.
You mean apart from section 3.1?
If the ash cloud is forecast to cover the entire region then they suggest that operators avoid the entire region. It's quite simple.
So why not at least send mil A/C up there by daytime VMC and let them look for the actual location of visible ash clouds and keep airliners away from those area's?
Because the ash is not always visible. Right now above my head (Copenhagen) we have ash that is slightly more dense than that which affected the NASA flight mentioned earlier, but I can't see it - either by looking up from my office or down from a visible light satellite sensor. You might be able to see better by using a FLIR, but that's not guaranteed.