When should I cut my tree down?

I have a monster of a tree in front of my house, the size of a 4 story building at least....Its dying. A few years ago woodpeckers spent 2 months covering it up in bullet holes. My friend who is a forester said they're only attracted to dead trees, so they must sense some rot or decay coming from it. Sure enough, the branches are showing this now. The branches from the bottom to half way up the tree are half brown...by this I mean the branches are brown leading away from the tree half way, then the remainder of the branch is still green approaching the tip of the branch. The top half of the tree is starting a little, but its still mostly green, in fact its still producing acorns up there. I'm not sure of the species of tree it is, I think its a douglas fir but not sure...the tree is not "branch heavy", meaning the branches are not climbable, so I don't think the weight of the tree will ever cause itself to tip over or anything. The trunk goes straight up like a telephone pole, so even if it were completely dead I think it would still stay up. So theres no safety reason it should come down....it'll just get really ugly soon, but even there its still pably noble looking for a few years more I should think. It may even take 10 years for all traces of green to be completely gone. Anyway, is there a time in a trees stages of death that makes it easier to cut down than other times? The tree can't be felled, theres nowhere for it to land, so it has to be pruned and sectioned.