snowman, I smiled with memory of my grandfather when reading your question. He helped me with my first car, a '70 Nova when I was 16. Exact same problem. I drilled out the broken stud while the manifolds were still on the engine and I was lying on my back under the car.
If the above methods don't work you are going to have to drill it out. If you drill right in the middle of the stud then you can peel the stud remnants out of the manifold and save the original threads. If you miss and damage the manifold then a helical thread repair insert will fix it.
Grind it off flush, center punch, drill it out. Start with a small bit, then step up to 5/16, which is the tap drill size for 3/8-16. Your studs are probably 3/8-16. You must drill it right through the center to save the original manifold threads. If you have an easy-out, you can try it when the drilled hole is about 1/4 but I haven't had much luck with easy-outs.
