Booleans are rubbish . Use NURBS if you want to do this cleanly and easily.

Look into Trim tool, planar tool, Fillet Tool, curve projection, curves on surface.

Basically what you want to do is get a nurbs plane and project a circle onto the surface and then trim the surface making a hole. You can then use duplicated versions of your original curve to give your hole depth, duplicate it off the surface and create depth, Fillet would be used to make it smooth etc.

making something like this :