If it will not come out with a reverse bit or an easy out. A trick (if you have acces to a MIG welder) is to weld a larger nut to the broken bolt. If it's a 3/8" bolt, use a 7/16" or 1/2" nut so you can get the MIG in there to weld it. The heat of welding will help loosen it up, just let it cool and it should spin right out with a wrench.
It may be a little hard to do that in the car, but no harder than trying to dril a straight hole while leaning over the fender.
I've used Helicoil with pretty good luck - but usually for stripped threads. You could drill the broken one with the drill bit that comes in the helicoil kit - then tap new threads and insert the coil.
Working on that mounting plate is not going to be a easy thing to do just because of where it is. If the bolt is broke flush or recessed below the surface its going to be one hell of a trick to weld a nut on it. If it is broke flush take a sharp center punch and try and get a good hit as close to center as you can. If you have to drill it you will need an angle drill anyway, a good sharp twist drill will cut a Gr.8 bolt easily. Every once in a while you get lucky and you can "chase" the bolt with a small chisel or punch. Good luck.
You can weld a flat washer to the bolt first. It is easier to get a good weld on the bolt like this. Then weld a nut around the outside of the washer. This almost always works for me. Drilling usually results in damaged threads.
'69 RS/SS396 pro street