The oil slick wasn't from the plane, it was ship fuel, not jet kerosene

I know I'm speculating here, but most ATC radars rely on transponders rather then skin paints to track the aircraft. The 777 has two sets of transponder antennas and communication antennas.

It seems unlikely that both sets were damaged simultaneously in anything but a catastrophic failure, and more likely that the transponder, radio, etc were turned off or disabled.

If you look at the pictures from Pan Am 103 (lockerbie) which broke up at 31,000 feet and TWA 800, which broke up at 16,000 feet; note the large pieces and significant floating debris. The fact that they have not found debris after 3 days of searching indicates it probably did not break up in flight.

Of course, I'll probably be proved wrong when they find the thing.
Hope for the best and prepare for the worst.

The object in life is not to be on the side of the majority, but to escape finding oneself in the ranks of the insane