Do you know if the exhaust manifold bolts are broken just under the head of the bolt, or flush with the cyinder head?
Reach in through the wheel well and grab the corners of the heat shields, and feel underneath the loose corner(s).
If you only feel the thickness of a nut, the bolt is broken at the thead of the bolt. Easy-peasy to remove.
If you feel the body of the bolt still attached to the shield, it's broken flush with the cylinder head. Weld-a-washer-and-nut is the best method to remove the broken stud.
I do not recommend drilling out the broken stud unless you have a drill template and are experienced using left-hand drills and extractors, it's way easy to ruin the threads or worse, drill into the water jacket.
As
@Ken226 said, belt-sand or machine the manifolds flat, replace the gaskets and hardware
(and no, you don't need fancy grade 8 bolts for the repair, they only torque to 18ft-lb or so), and you'll never have another issue.