What you describe makes one wonder how they every found it stable enough to drill in the first place. This is a stinking pipe in the ground, not a volcano. It could be
buried given enough rock. Particularly in nearly two months time. imho
Dumping rock onto loose sediments wont do much good. Closing the well with a landslide apparently will require a nuke. Here is a video showing how the Russians do the trick. Those Russians can apparently get away with murder.
You can bury it, but what then? Anything you can dump on it will leave pore spaces in the pile, and the oil will continue to escape through those pore spaces--just like it is doing in the formation it is coming out of.
Nice idea, but it doesn't solve the problem.