milky radiator core - how to remove?

[v6dreamer]

is there a way to verify head gasket failure w/o removing the head?

You can check each cylinders for compression test.
Or....
Take off the radiator cap and look for bubbles when you first start the car and the engine is cold. You can also buy a block checker kit from an auto parts store, they are about 20 dollars here, dont know in the Phils if available or how much. They are very simple to use, you put some of the fluid its a little bottle, take off the radiator cap and push is the bottle, start the car and watch to see if the fluid changes color.