Sit down with the violin held against the chest so that the bowscrew will touch your leg when you do a sautillé stroke.
Holding the bow by the screw is an excellent practice technique that can be used for all bow strokes when you suspect that the bow hold is causing problems.
While playing sautillé the bow hand is not floppy, however it is useful to think of the whole hand being open; feeling that the base knuckles of the thumb and fingers are opening out and releasing away from each other. The thumb especially needs to be flexible.
Holding the screw tends to neutralise any unwanted tightening in the bow hand. Once the stroke is working use a normal bowhold....