One of the things that can go wrong is if you decide to take the tree down whole, as you are making the cut, the tree can implode on itself from it's own weight. Remember how the towers fell on 9/11, well it would start off kind of like that, but from the bottom up. The failure could continue for several feet until the end of the hollow, at which point anything could happen.
You see, even if you have a rope secured away from the house, the tree dropping straight downward would immediately slacken the rope, and now the tree can fall whatever direction it happens to be leaning.
If it should fall towards the house, at some point the rope will tighten up and steer the falling tree left or right of that, if the rope dosen't snap, and the tree will take a fast sweeping fall. Imagine a huge 10,000 pound windshield wiper, moving at 50 mph. That's what you'd be looking at coming at you, with no time to react.
Of course this assumes that you weren't crushed to death by the initial implosion.
Another common occurrence with hollow trees, is barber-chairing. This is where the trunk splits and sends part of the trunk shooting straight back. Imagine you flicking a fly off a surface as hard as you can, only you're the fly and the tree trunk is a set of giant fingers.
One way to avoid the forces described, is to remove the limbs and take chunks off from the top down. But if you think the tree could fall on your house, what makes you think it can't fall while your up in it creating huge shock loads from cutting limbs?
A qualified arborist would most likely bring in a bucket truck and have this thing on the ground in under an hour. If you did the clean up, I'm sure you could find somebody to do it for less than $500.
Our bucket truck rates are about $200/hr, and we're in a pricey area of the US, not like NY or Chicago, but I'm sure more than you out there in the Boonies.