Definatly a fun one to trouble shoot. When you say you diluted your power steering im assuming you took as much of it out as you coukd then refilled it. Have you asked for anyome to look at the fluid levels when you turn the wheel? Almost sounds like theres an air bubble forming after running for a while. Maybe a problem with the valves in the pump itself which may be sensitive to the rising heat in the engine bay? Have you noticed if it gets worst gradually perhaps?
I would suggest trying to bleed the system first and proper refill. Then replacing the pump if it doesnt solve it.