The drive side is reverse-threaded. A very large reverse easy-out is hard to come by but would be the correct tool once you had it apart.
Lacking a reverse easy-out I'd try using a step drill (Uni-Bit) to bite in and either turn it right out or at least take away most of the material as a first step of cutting it all out.
I bet the uni-bit would get it out eventually before you ran out of material to drill out and if you did run out of material stop before you get to the BB threads and switch to a hacksaw blade and cut a small notch or two. This should weaken the cup enough so that it will loosen with ease with a bit of pounding with a cold chisel.
On regular right-hand threads that are stuck and need to be drilled and easy-outed I always start with a left-hand drill bit. 8 out of 10 times I never have to go to the easy-out as the left-hand drill loosens it right up after pulling out some material and reducing the stress on the threads. With the reverse-threads of the BB drive side a right-hand drill or uni-bit will have the exact same effect.