I didnt see anywhere did you mention of it was burning or leaking oil. I mean with the amount you are losing, it sounds more towards leaking and not burning only because of the rate you are losing it at. I also didn't see it mention that they checked the front timing cover seals or anything simple. Sounded like they just went straight to a HG. I mean they could always an exhaust test where the hook a device to the coolant reservoir. This device uses a liquid that changes color that determines if there are exhaust gases leaking out of the combustion chamber. Not sure if this test is possible for our trucks, but ive seen the used on Mercs and Audi's without a problem. I'm not convinced the HG was even the problem.

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2011 E70 50i M Sport