I just girdled some (small) trees in an underbrush area I have. I took all the bark off all around the tree--about 6 inches wide.
My observation was that you could see the effects pretty quickly, but the effects weren't uniformly even. Some parts seemed to die a bit more quickly than others.
Now granted, these were smaller trees and not big ones like you'll be working with.
But I think the risk is that instead of a whole, healthy tree, you'll be cutting down a tree that has parts that are more dead than others (potential falling limbs?) and I think that would cause more hazard and more variability when you cut it down.
The upside to girdling is that you lose the vegetation and make the are less shady. The downside would be that it might make the tree more difficult and more hazardous to cut down, increasing the chances for injury and property damage.
I don't think the potential convenience of doing this is worth upping the danger (even slightly) of cutting down the tree.