Much of my high wind gybing occurs on pretty much the same stretch of water: just north of Treasure Island heading east after a day sailing San Francisco Bay. 12 knots is a light breeze here. Usually blowing 15 to 20 when I do this. Most times is port tack downwind. I head down to a wing & wing, thus the jib's now on the port side of the boat with the main still full out to starboard. I don't trust the autopilot going downwind, so use the wheel brake lightly. Crank in the main after centering the traveler. Slowly turn the wheel to gybe the main, let the mainsheet out, adjust traveler and jib sheet as necessary depending on new course of either broad reach, beam reach or close reach heading south. Take wheel brake off, reset AP.
I find it much easier to do the jib first when it's really windy. In lighter air the jib can wait.
Only guy I knew who hadda do "chicken" anything was a friend with a 27 foot schooner - yeah, that's right. Not too many of them that small. 270s were required to TACK!