It would seem to me that there is a fairly simple (in the sense of "if I had many millions of dollars, desperation, and the resources to make it happen, this is a lot easier than a lot of other approaches) method to not stop, but nearly completely contain, this gusher.
Clearly the problem isn't getting some kind of pipe down to the area in question; they've done that multiple times. So let's envision getting a pipe very near to the wellhead. From the pipe, a short (relatively) section of flexible pipe, and at the end of that, a wide bell-shaped section of flexible material.
At the top of the pipe, a very powerful pump capable of pumping more volume per second than is emerging from the wellhead.
Start pump running and get bell-shaped section over the wellhead. Maneuver until reasonably centered and then let it drop.
Flexible section is suddenly drawn in to adhere to the wellhead and all surrounding material by the suction. The oil is drawn up the pipe, mixed with some amount of water that leaks in from the not-perfect seal.
Have on station two tankers or processing boats which can handle the volume such that when one is sitting there catching the 90% oil, the other is taking its full self to some location where it can be unloaded and processed, then come back in time to relieve the first one.
The flexible pipe and bell should be relatively cheap and easy to replace, so that if the combination of oil and seawater erode it, they can be replaced easily.
The basic principle should be clear for anyone who's used a vacuum cleaner and had it suddenly get stuck on a curtain. It's not particularly ELEGANT, it's a patch job, but it should WORK. You shouldn't have to be pumping against the pressure of the ocean -- you take the water off the top of the column, the volume is mostly replaced by the welling oil, etc., so you don't need some incredible super-pump that manages a hundred atmospheres of pressure or something.