Here is how I tacked my H16 in heavy wind. Most of the time I was solo (I have a "heavy wind" build) so that may have made difference.
1) Fall off a bit to gain speed
2) Using gradual rudder inputs, begin turning into the tack. While doing this sheet the main in to keep your speed up.
3) Keep the jib backwinded. I had to cleat it since I was out of hands.
4) As you come head on to the wind let out about 6" of main sheet, maybe more depending on your situation.
5) Immediatly after this move to the new windward side of the boat.
6) Leave the jib backwinded until the main battens "pop" across (you will actully hear them do this). Then, bring the jib over. Do not over sheet, you want it to have some shape to help accelerate you.
7) You may have to let out more of the main at this point. I found this to be true especially in high winds.
Once you start moving forward again fall off some to gain speed, the head up to your course and trim the sails appropriately.
I am not a racer. Most of my H16 time is in the ocean off the coast of Salem and Marblehead, MA. My tacks were not always lightnig fast, but I did get around 98% of the time. Much of tacking the H16 has to do with timing.