The higher highway speed increases the ram air effect and the cooling on the radiator. This is compensating for a partially plugged radiator. At slower speed of 30 mph there is less ram air effect, the electric cooling fan turns on but it still cannot pull sufficient air across the radiator to cool the engine properly. Because the radiator is partially restricted in effect you may have a radiator with heat exchange surface area that is 1/2 of what it needs to be. You need to replace the radiator.That is what so frustrating. I can operate the car at 80 mph (interstate) on an 80F day and it actually runs cooler than it does at 30 mph.
Going to an external transmission cooler is not really going to solve the overheating problem? Where are you going to mount it? In front of the AC condenser? If you mount it there the heat of the transmission is going to cause problems with condenser heat exchange and not allow the AC to cool the interior of the car properly. If you mount it in another location then you will have to provide a fan to draw air across the transmission heat exchanger when you are driving at slow speeds.
One way to test a radiator is to remove it and take it to a radiator shop and have it flow tested. Of course someone at the radiator shop will have to know how to do this. I doubt if you can find someone knowledgeable today to do that and find the proper specifications so as to check the radiator flow. And there is some cost associated with this.
You could remove the electric cooling fan assembly and shroud from the side of the radiator that faces the engine. Reconnect all cooling system hoses and make sure you have the proper coolant level and no air trapped in the system. Start the engine and let it idle until the thermostat opens. You could carefully feel the back side of the radiator and try and find areas which are cooler than others. You have to be quick in doing this as you do not want the engine to overheat. If you find many of these areas that is an indication of a blockage and no coolant flow. An alternate way is to use an infrared heat sensing gun and aim it and various areas on the radiator and find colder areas which would indicate blockage.