I spent some time last night taking apart the rudder's trailing edge.
The process of drilling out rivets is pretty simple. If you haven't seen one before, a rivet has a broad head and a cylindrical body. You drill partway down the body, use a pin punch to pop off the head, and then push the rest of the body through the hole. The tricky part is you don't want to make the hole any larger, or the rivet you put in there when you reassemble the thing won't hold properly. I usually have a problem with the drill bit trying to walk a bit off center when I start drilling, so I use a center punch to make a starting dimple in the center of the head. It's not perfect, but it helps. I also check often while drilling.
After a lot of careful drilling, I eventually managed to drill out all the rivets without enlarging the holes. Here you can see the wedge that goes between the trailng edge skins. What you can't really see in the photo is that the wedge has dried T-88 epoxy on it. (So do the skins, but not as much.) The web site for the epoxy manufacturer says you can remove dried epoxy using a suitable paint remover. So there's now a quart of Certified Coatings Sure Strip paint remover on its way from Aircraft Spruce.
By the way, Aircraft Spruce was most helpful with this order. According to the epoxy maker, "suitable" means the paint remover must contain methylene chloride. I couldn't tell from the Aircraft Spruce web site whether Sure Strip contains methylene chloride, but the folks at the Aircraft Spruce order desk went into the warehouse, pulled out a can, checked the contents, and called me back to confirm that it does.