I finally admitted defeat and called in a professional. State Farm will cover the cost of removing the broken limbs and repairing the garage roof, but the big pecan tree really needs to come down. Well, at this rate, it will be down soon, but it really needs to come down in controlled environment, not one limb at a time. The "tree guy" gave me on quote on taking it down, removing the stump and cleaning it up . . . $1950 . . . so I guess the tree will remain standing for the time being.