I've had a few issues with the cooling system on my car as well. It overheats, but not all the time. I have flushed the radiator countless times, only for it to get "murky" within a month or so. When I first got the car it had a leaky freeze plug on the right side and I changed it. While the plug was out, I flushed that side of the engine out with a garden hose.
I adapted a piece of 1/4" air line and stuck it inside the engine. I am not kidding when I got about 10 ounces of rusty crap out of the water jackets. About a week ago, I did another freeze plug, this time on the left side. They are not popping from the cold weather, they are corroding from the inside out. They can be removed and replaced with little effort. I gat another 8 or so ounces of rusty crap, chunks and even some casting sand! No kidding! Casting sand! I took a plastic storage container and punched holes all the way around it about 2 inches from the top to catch the crap, but still let the water out without any loss of the material. I was amazed at just how much actually came out.
Now the radiator is the original Harrison unit and it still works, but has some minor blockage inside. Not one radiator shop will touch it because of it's age, for fear it will disintegrate if they pop the solder. I have looked high and low for another one or even a new one, but there isn't any companies reproducing them for this car. a 1960 unit will work, but these are few and far between as well.
My brother in law owns a company that rebuilds water pumps & clutches and he swears that the water pump is never the cause of overheating problems, even if they are not functioning. He is my age and has been doing this since he was 14, so I believe him.
So far so good! I strongly recommend water wetter or similar to add to the coolant/ water mix. This will drop the temp 20 degrees.
If anyone knows a secret place to find original radiators or a supplier for one, please post here for all to see.
Chad