Just go around the block. Just do it.
Why, you ask?
It will not take more time. I am watching you struggle through the various vicissitudes (and literal reverses) of the maneuver, and I am confident that circling the block at 35 mph would answer much more quickly.
You will not hold anyone else up. Yes, it's nice of that lady to wave you on, but you are currently delaying about six automobiles, not to mention an irate and terrified cyclist whom you obviously cannot see and about whom you obviously do not care.
And, finally, you will not be attempting an ill-advised and probably illegal stunt. If you insist on turning around rather than circling the block, find an actual driveway. Do not--I repeat, do not--attempt a three-point turn in the middle of a four-way intersection.
Honestly, what possesses people to do this? What part of this decision is not obviously deranged? And rude?