I like to think of cardistry has having certain 'focus' points.
When you're gripping the packets, focus on the 'focus' points. These are ANY points where ANY of your finger contacts the deck or a packet deliberately. If such a packet needs to move, then focus on improving the strength of these 'focus' points.
For an example, in a basic straddle grip the 'focus' points would be the upper sides of the outermost phalanges of the index, and the pinky fingers. Improve the strength there and you'll have a strong, non-slipping straddle grip. Apply this principle for every motion or grip or re-grip within the Sybil.
Secondly, extend the fingers. You want to have sufficient space between the packets.
Thirdly, you can try putting rubberbands around packets if you want.