Have you considered just having the tree removed and the stump ground out? From the looks of the Google map pic, you have several, nice trees in your and your neighbor's yard. Had the exact same problem you had with a home in South Carolina - lots of Oak trees, no grass. Got rid of half of them and not only did the yard improve, but so did the curb appeal of the house. Plenty of vegitation in front of the house, but not so much you couldn't see the house itself. Good luck with what ever you decide to do.