If the radiator is clogged with rust and corrosion, then it will not cool the fluid well, even though it is moving through the radiator. Basically it would only allow it to partially cool the fluid.
Here's what I'd do cause I hate tearing stuff apart and later find out that it wasn't the problem.
First, I'd pop off the radiator cap and start the motor cold. If the water pump is working well (I assume the thermostat is still out) then you should have a steady and strong flow of fluid coming across the top of the radiator and you can see it with the cap off. That should pretty much confirm that your water pump is working well.
Next, before pulling everything apart, run the motor until it gets overheated and then use a thermometer or some other gauge to get a "true" temperature of the radiator fluid. Maybe the dash light is not right and it's not really too hot. I don't know exactly what you did with the "replaced thermostat wires" but it's good to look at this systematically. You could choose from a number of tools to measure the actual temp of the radiator fluid, there are even super easy to use infrared temp measuring tools that you could borrow from a shop or friend.
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Then, if it really is too hot, to me, it has to be the something wrong with the only thing that cools the fluid - the radiator!