When trapezing down wind, you can not gybe from the wire. I'm pretty sure it is impossible if you want to gybe quickly. When you tack, the boat turns up into you. When you gybe, it goes bye bye, and you're left hanging in space.
Karl, try this... next time stuff the bows just before the massive gybe.. and peter pan around the forestay to the otherside...
Please report back and let us know if that helps.