Is it even possible to aim headlights on a 280zx? If so, how? If not, then how should I go about bringing my driver's side headlight back to where it is supposed to be without too much D.I.Y.?

I've seen headlight adjustment screws on various parts sites, but not on the actual car nor where they could have been.

 

Yes, you can adjust them. Look at the top and outside edge of the headlight hole in the bucket and you will see a groove for the screw, look in and you will find the screw. Adjust.

There's also a detailed "how to" in the FSM: XenonS130 - S130 Factory Service Manuals