The first item I like to check is temperature differential between the radiator tanks. This checks cooling capacity of the radiator. The coolant may flow to quickly thru the radiator ( not giving the coolant enough time inside the radiator core to cool sufficiency ). There should be about 12-15 degree difference. A couple things come to mind while reading all the posts. Here in Arizona we are aware of the cotton type radiators. These do work well in an enviroment such as cotton gins or cotton processing. They still need to be maintained. But When we have an enviroment that has overheating issues. We will recommend at least a four core type radiatior. This will usually take care of any high heat problems here. When the ambient temperature reaches 115-128 degrees; as it does here in the summer, this type application can be severe.
Working for Yale dealership we have limited access to Toyota & Nissian units. But I believe these water pumps also have a bleed valve to bleed the air from the system. I would also check to make certain there is no air trapped in the water pump. This might cause reduced or no coolant flow. I hope this input is of some use.