I think you forgot to burp the engine. Near the point the upper radiator hose attaches to the engine there is a nipple that looks like a brake bleeding nipple. Loosen it half a turn or so and leave it open until a steady stream of coolant comes out. Close the bleed nipple, top up the radiator and give it a try.
The idle becomes unsteady if there is a bubble in the coolant because the thermo lift valve opens until hot coolant hits it, then it closes and the coolant drops back down so the valve opens, over and over. Bubbles also prevent the coolant from circulating, especially at idle, thus the overheating.
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