Have you considered mounting an AC through the wall instead of through the window. If you go this route and decide to mount it higher on the wall make sure you make allowance the roof eave before you cut the hole! (ARGH!!!)
I have installed 2 mini-splits in my home. One is a 12K unit in the great room. The second is a 3 head unit for the 3 bedrooms. The efficiency gain that Bill quoted seems quite low to me but I purchased top of the line Fujitsu and Panasonic mini splits with top end SEER ratings. Cutting a hole in the wall to install a through the wall AC was a heck of a lot easier than the mini-splits.
There are also the portable air conditioners that exhaust the hot air through a flexible duct:
portable-air-conditioner.jpg
That might be a much easier way to put an AC in a casement window and have it easy to remove when summer is over with. I think the efficiency is usually quite low on this design???