my 2 cents..
There are several types of koshinage and they differ by how uke's arm are positioned as the technique comes into play. Some variations have uke's arm positioned in such as way that uke can still grab hold of nage's lapel before he goes over nage's hip, helping him get into position for the throw. Uke' grabs are far uder nage's torso as possible so he sets up for the throw. This gi-grabbing technique also helps make aikiotoshi a little safer.
The other variation does not allow uke the opening and so uke can't grab hold of anything to ease the fall. This variation is tougher to practice but a lot of breakfalls doing other waza help "wire" that flipping movement that is the core of the breakfall. Uke has to instinctively flip for the breakfall before trying it out on this kind of koshi nage.
For both types, as nage I "sight" up the arm before I "drape" uke over my hip. I look up along my raised arm to make sure that it's straight. This also forces the side of my hip closest to uke to drop down just as uke comes in contact with it. As I drop my raised arm, I "seesaw" uke over my hip.
Hope that helps..