Ok, so what steps am I looking at to get this where it needs to be? I thought I could just drill the heads off, pop the case, get the stubs out with pliers, and then replace the cover and gasket. Does that sound right, or is a gremlin going to jump out of their, slap me in the face, sleep with my wife, and screw up my ride? 
Mystic is right. But if (when) you get the heads drilled off you've got a ways to go.
I think you're thinking that the 3 screws hold on a cover? A common misconception. They simply hold the field coil (electromagnet) in place. The cover is the big thing held on by 8 or 9 screws. And if those 3 are giving you so much trouble, I hesitate to think what the next 8/9 will be like.
And as i said, I think the tranny cover has to off as well.
If you pop the heads off the 3 screws you can't go any further without taking off the BIG cover, getting the field coil out and then getting the stubs out.
Once you get the big alternator cover off, there is the reduction gear for the starter drive that will fall off. And the wiring for the alternator you will have to deal with. These are not big deals, but you asked and they are there. You can do it.
You should put a small shim under the centerstand to tilt the bike to the right just a few degrees. When you take the alternator cover off, oil will come out and you'll need a drip pan under it. By tilting it you will limit the oil to a minimum, less than 1/3 cup.
Ultimately those three screws do hold on the finned cover you're trying to install, but that's just for looks. A long way to go for a look. But it needs to be done.