Drilling out the nipple or any screw to the root diameter of the thread and then picking out the remaining thread can be difficult. First you need to be certain that you are drilling dead center or you will wipe the threads off one side. Easy outs are great if they work but dont break one off as they are hardened and can't be drilled out if you break it. Being a welder I use a different method. Using a TIG welding torch I build up a small tit onto the broken screw untill it is large enough to grip with a vise-grip or weld on a nut. Then I attempt to back the screw out. The heat from the welding is often a benifit to loosening the screw but not enough to cause melting problems like you describe. I have done this hundreds of times with great results. If it does not work you are no worse off than you started and you still have the option of trying to drill out the screw. When it does work you have a perfect and original tapped hole left to install a new screw or nipple into.
Bill G.