How can I manage a drop ceiling potentially overlapping the top of a window?
I had an almost an identical situation as you have shown except I worked very hard to eliminate the amount the drop down ceiling came down and was able to get it to work at 3.5 inches. I the built a wood box as shown in my diagram below that allowed the drop ceiling to fit around the box but still allow the window to exist full size. 



This picture is a side view looking into the edge view of the window unit. The box is typically made of four pieces of pine boards including the top, two ends and the front face that parallels the window. The amount of projection out from the window will depend upon far back the window surface is from the wall surface and how far down the drop ceiling comes.