I eventually got tired of the poor performance and even worse shadows. So I googled turn shadows off skyrim and found a way to turn them off completely. My FPS instantly jumped from 30ish to 60ish. I was so upset. Bethesda royally messed up the shadows in this game. They look like garbage and take up all of the already restricted resources that the engine utilizes.
The game engine is simply not optimized for PC. It seems to use only a fraction of my computer's available resources. It's basically a console game made available for PC users with none of the advantages of being on a PC. The screw up on the shadows combined with the screw up on the lack of resource usage just combined together to make Skyrim perform very poorly on PC.
Flame-retardant appeal: I know, I know, making games is hard and all that. This is not intended as a flame or a troll post, just a hopefully helpful tip for PC-users with the same problem. Google turn off shadows, for +30 fps. (Since posting links to editing game files is frowned upon I won't post the link. It's an ini file, nothing major, just back it up.)