Ok Mike,
So if taking your datum where PE and KE is zero, where does the energy come from to zoom climb? In your example both PE and KE increase. The energy to do this must come from somewhere. If not, I'd patent your findings and make Bill Gates look like a pauper.
A turn in the hover is not an aggressive turn as you describe it. It is completely different mode of flight as the pilot is intentionally maintaining groundspeed. Airspeed is irrelevant in this case (subject to aircraft and power limitations). In the downwind turn being discussed the pilot is maintaing airspeed.