Good call. on getting a Tree Service to drop it. If they're just dropping it, and you're processing all the wood, it shouldn't be that expensive. Plus, you'll have a lot of immediately burnable, or sell-able firewood.
I dropped 20 to 30 trees on Saturday ( some kind of Pine blight ), with my neighbour. Some we dropped onto the road, and chopped up, some we dropped into the woods, and left them as is. A couple were bent over, like your picture, those, we just walked away from those .. it just wasn't worth the risk.. at all .. I'll dice them up when nature drops them to where I can deal with them with my feet on the ground.
Keep safe.