I'm going to mention something that no one else has.
Getting the kite out past the edge of the window a little by stepping back and pulling on the lines, and then turning the kite down into the slide
, really helps in getting the kite moving back towards the center of the window.
When a kite is stalled out near or even past the edge the wind is hitting the sail obliquely which causes the kite to be pushed sideways.
Makes life so much simpler.
Also, if the wind is up this may be the only way to get the kite to slide in the first place. In this case be prepared to move in diagonally towards the center along with the kite to maintain the stall.
The reason you don't have to do this so much in light wind is because of the reduced size of the wind window: the edge is basically right in front of you.
The fact is you will get a much stronger slide in slightly higher winds. You just have to be fast enough on your feet to keep the kite stalled and moving.
The ability to move in on the kite is the limiting factor on how high a wind you can slide (or stall) a kite in.
"Feets don't fail me now
So just how fast are 'ya?