Flump,

Try this for the spinnaker gybe - don't float the spinnaker out as the boat turns but just as the spinnaker starts to backwind, tug the active sheet hard, then go across the boat taking the lazy sheet (the new sheet) with you and reel it in. The tug / pop just before the spinnaker deflates makes the luff fold to the new side without wrapping around the luff - gybes are much faster. The timing of the tug is critical however.