It could be a typical indication that all cooling air through the rad is lost when you stop at the light. Thats if the fluid filled clutch that holds the fan is shot. This would also allow the engine to store more heat up all the way up the hill than should be present.

With the engine at normal operating temperatues it should stop the fan turning fast when you have someone shut off the engine. Also when hot with the engine stopped see if you can turn it with the fan blades easily by hand. Remember the fan clutch is controlled by temperature.

If the fan fluid clutch checks out as good. You could source a new radiator youself and install it for a lot less than you have been quoted I suspect. You will have to get your hands dirty though.