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You said you replaced the entire cooling system, so this means we can count out any blockage in the radiator ,bad water pump , and thermostats sticking , if these have all been replaced and are all good then i suggest you have the system checked for co2 in the water / coolant . n

Not having oil in the coolant or coolant in the oil does not mean you have a good headgasket .

What has most likely happened in your case is the gasket cylinder ring has blown to one of the coolant channels ,when this happens co2 gets into the coolant system and overheats the engine , you can see signs when you have the radiator cap off the radiator and run the engine , when you run the engine the following could happens and is a sign of a bad head gasket ,
1 coolant will be forced out the rad neck or you will see bubbles coming out the rad neck., but the best way to check this is with a combustion leak test kit .
Or take a drive down to AutoZone and they will do this test for you.
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Kind regards Greg.