I finally managed to get a window unit installed in my bedroom, which is making my bedroom much more comfortable now. I was somewhat at a loss for a while because I had looked at installation instructions, and they seemed to include all sorts of bits to screw into the window itself. These are of course not really my windows, so I was a little hesitant about this. But after talking to people at Sears and Lowe's, I decided I could just ignore the bits about putting in screws and bolts (at least for a small unit).
However, I still had a thin rim of the window which juts up out of the sill over which the unit has to fit. (This is pretty standard. It's just what the window slide down against when it closes.) Unfortunately, no manufacturer seems to make units with any sort of groove or channel to accommodate this. The standard recommendation is to lay a 2x4 along the window sill and place the unit on this. So that's how my unit is set up now, and I have ignored all the instructions about screwing or bolting anything to the window itself. If it falls out and kills anyone, I'll let you know.
Of course, all this begs the question of why the manufacturers of window units don't build the units to accommodate what is apparently a fairly standard window design, and instead suggest that you jerry-rig it with a couple of boards.