So, yea. My hand is really sore now. It appears that in Keeper's pics, the window adjustment screws cannot fall in in his model year. On my 05, they can, without any warning, and like people said, can only be put back in from the inside of the door. Great.
To echo what Viper said, here are the directions I followed. With the window up:
1) Remove lining panel (4 top hex screws, 1 front plastic Philips screw under the sill of the front of the lining, slide panel towards rear of car)
2) Remove 3 screws (2 big, 1 small) from door handle plastic silver-ish lining
3) Remove 2 screws (2 big, same size as above) from door handle
4) Push door handle up towards roof with non-dominant hand
5) Reach into door and feel where the hole is. Stick a screwdriver through the hole from the outside so you can find it better. You will feel the panel/rail that the screw pushes against, so you will have to move it towards the outside of the car a bit to get the adjustment screw in.
6)Hold screw carefully between forefinger and middle finger with the head with the adjustment slot towards the inside of the car.
7) Reach into door, loop thumb around panel the screw pushes against, and push to outside of car
8) Using deft dexterity, wiggle the screw into the hole you found earlier
9) Let go of door handle, bracing for pain. Use screwdriver to turn screw counter clockwise back into hole. The angle is tricky, and you will need to push in from the inside of the door
10) Swear, drop the screw a few times, repeat, and you will get it. Once I got the procedure down, it only took like 5 minutes, 2 curses, and, oddly enough, no blood.
The best part is, once you get it back in, you will know it is near its maximum deflection, so you shouldn't have to screw it back in any more
The back screw is real easy to reach, although that one doesn't seem to fall out. B*stard. Some days, I think my Elise just wants to mess with me...