I doubt anything with an Arduino will help - I do wonder if this idea has been considered (and I realize this is all "armchair"):
What if (perhaps via one of the relief wells, or perhaps straight into the damaged well) they injected liquid methane or propane into the well - at that depth and temperature, as soon as the methane/propane hit the water, shouldn't frozen hydrates form, plugging the well with a frozen hydrate plug?
/very armchair, and I don't understand the physics/chemistry involved...
//oh, and put an Arduino on it to monitor gas flow...
What frightens me most is I had the same idea as cr0sh! Even went as far as trying to find the phyical properties of methane clathrate. Think I got distracted by something shiney though.