I have done similar approach except without the tube. I used a drill that fit snugly in the manifold hole to simply form a dish in the broken stud. This dish will then center a small (~1/8in) drill bit to allow you to drill a small hole in the exact center of the stud. Using progressively larger drill bits, I kept enlarging the hole. With some luck and PB blaster, you can use an easy-out to back the stud out of it's hidy hole. Be careful though....if you break the easy-out, you know have a hardned steel piece in there to deal with. If the easy-out doesnt work, then keep enlarging till you get to the right tap size and just re=thread.