I'll preface this by saying I'm very proficient with a hand drill and do not use easy outs. I would start by drilling the head off. What's nice is the stripped hex should keep you close to centered, the bottom of the hex is tapered to a point which will also keep your bit centered as long as you stay parallel with it. A 3/8" drill bit will get you do the outside diameter of the threads, but I would start with a bit that fits closer to the stripped diameter. So from the face of the screw you will need to drill in a heavy 1/2" depth and then the head will either fall off or you can pop it off with a cold chisel. Then the real work begins, working the manifold to break free the white powder of death that causes the head to strip. The getting the rest of the screw out. This could all be a crap shoot so be forewarned.
Head length of screw is .388"
Angle point of a 3/8" bit is roughly .125
Total drilling depth = .513" deep
Next hard part, getting a drill and bit in there, you might need a right angle drill. Not sure I would want to do that in house like you are, I would have pulled the engine. Also for the next time, degrease the engine before you open it up.