Replacing Radiator, should I replace it THEN do an engine radiator flush

Right and since I dont have access to a hose. I'm hoping this will be enough to clean out without sticking a hose thru the block: Whaddya think?

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That'll clean surfaces, but it won't do squat to get the rust sediment out of the block and around the cylinders.
It's not just dirty coolant you need to try and get out, but more about sediment and that flush chemical won't help that part one bit.
Like I said earlier, you would be shocked what comes out of a block with the combination of water and air both.
Around the bases of the cylinders is where the highest concentration of heat is in an engine, and also happens to be where sediments collect and cause hot spots due to insufficient coolant access.

But a man has to do what a man has to do with what he has to do it with.:D