Well, despite what our one neighbor and we said, our other neighbor went ahead and cut the tree which was overhanging our driveway. He pointed out that the tree was probably too low for his stock trucks to pass. So, he cut it down, but it all worked out well. There is no soil slippage as I had feared. (At least not yet.)
After David had cut through the log, he then hooked a chain to the stump and his truck and tried to pull the root system into our driveway, but it would not budge. The root system is so large that it is hooked behind a smaller gum (eucalyptus) tree and a rather large gum tree. Those two trees will hold the root mass in place, at least until one or the other of those two trees also falls.
So, all’s well as ends well. Or as we say here in New Zealand, “It’s good as.”