Brace yourself, I'm going to go further into conspiracy land, but there's the possibility the end goal wasn't just to steal a plane for scrap metal, or to use it as a ride for the local fair. If that's the case, you'd want the world to continue thinking it disappeared in the ocean, and you don't want to raise any alarms by taking credit.
The 777 is a fairly common long distance aircraft. Would it be possible to give it a new paint job, and then in similar fashion to the OP, fly in the shadow of an existing flight?
For example, you paint it up like a Lufthansa 777, and then try to follow one of those flight paths at some point between London and New York. If anyone gets a visual on the mystery plane flying into US airspace, it looks like a commercial flight simply not responding. Not quite as suspicious as a jet or military aircraft. Would they shoot down a commercial 777 that's flying a standard route, with no indication of it being hijacked, or a threat?
I'll admit, the above idea is absurd, but this entire situation is making little sense. I hope we get some answers one day.
Edit: A lot of people are saying in other comments that hijacking a plane isn't an effective method of acquiring a 777, or stealing cargo, or kidnapping people. However, it's been 10 days, and we simply know the plane disappeared. That seems pretty effective, a 777, 230 passengers, and cargo, all gone, and no one even knows if they were targeted, or if the plane malfunctioned and crashed in the ocean. If any of the above were of value to someone, it wasn't only effective, it was near perfect.