what would it cost to rebuild/overhaul the engine on a 2011 vw gti

Has this vehicle been evaluated by a professional technician? Don't be sure sure that you need an "overhaul". By the way, it's rare that anyone will overhaul an engine like this locally. Typically you can purchase something "remanufactured", or obtain something used. If money is no object, someone can go through your engine and "overhaul" it. But the cost of labor makes that prohibitive typically. I'd say locate a shop -- or two -- near you to evaluate what is going on and give you good options.