I have real trouble gybing out to sea when over powered in 25+ kts and rough choppy water. I find as soon as I bear away the board picks up heaps of speed and starts bouncing around on the chop feeling unstable, and struggle to initiate the turn.
Sure I could change down sails and life is much easier, but the gust may only last for 30mins so I prefer to ride it thru.
What can I do to improve?
I have the same issue in choppy water.
I find I start to turn downwind then the board takes off and bounces downwind usually ending up with me falling off the back.
The only way for me to deal with it is to try to time the gybe onto some chop or a wave so I can bank into the turn using the face of the wave and hopefully getting a bit of flat water to do the turn, plus making the arc as tight as I can even if that means losing speed.
don't bear away before starting the turn, start from a reach and just do it - maintain the carve from the very start
sheet in hard (oversheet), wieght forward, laydown style - if you keep the rail engaged it won't bounce
Bend your knees!!!!!
Really really bend 'em - heaps. Really exagerate the bend....and.....
do the exact opposite of what all of your instincts are telling you; over sheet the sail hard and aggressively, and carve hard into the turn. This is frightening but this is how you do it.
The quicker you can get from your sailing position into an over sheeted (sail stalled) position, the quicker you are safe from bouncing out. This is how you avoid the tentative semi-broad reach, am I or aren't I, "when will I slow down" position.
Straight from Guy Cribb school of gybe.
"you will know if the knees are bent enough, you will be below boom eye level. If you can see at, or over boom, its not enough knee bend"
IMO, when the wind is strong and the conditions are bumpy/choppy, the tighter the turn must be.
You must aggressively carve the board with extra foot pressure on the downwind side so that you are turning in a much smaller arc than a usual gybe.
The rig flip is also much quicker and therefore timing the release is important.
The process is made a bit easier by using either swell or a piece of chop as a ramp.
Cheers
Pull down into the boom to maintain mastfoot pressure + what others say..I can't do it 
very well but thats what Cribby says..It should help stop the board bouncing.
Guy Crib covers this topic in the latest Windsurfing magazine,I think he said it is also on his web site.
I'll usually wait for a slight lull in the wind, and with our crappy conditions they are often plentifull and or find a smoother pocket of water and gybe tight.
I usually just fall off.
Oh,.. you asked "What can I do to improve?"
I suppose that would be, try and fall off more gracefully.
I hope that helps. 
If your sailing offshore,ie a wave board- aim to bare off on a swell or wave.
Believe it or not the added speed,if you can control the board,makes it easier to flip the rig
As the apparent wind swings forward and in doing so the rig feels weightless.
If gybing in choppy conditions i find the easiest way for me to control the board in a turn,is too reach my backhand as far down the boom as i can...past the outhaul cleat.
This has the effect of adding the full weight of the rig and rider to the leeward rail forcing
More of the rail into the water thus giving more bite...at the same time the front hand is grip over and pulling down Wards this and bending the knees and leaning forward are imo the keys to control in chop.
This technique should work for slalom and wave alike.
Try reaching further back on the boom (with the back hand)next time you gybe and see if it works
My 2 rupiah worth.
Get down low, and go, go go!!
Bend the knees, and really concentrate on keeping the board carving around the second half of the gybe.
If I'm really over powered, I'll flip the sail earlier than usual, and coast the middle third of the gybe, then grab the other side of the boom, squat low, and power out the final third.
Best advice I was given was;
1) move your rear hand back as far as you can
2) go into the gybe full speed, that way the sail effectively ends up going faster than the wind and feels light.
Use the swell to help turn the board.
Good luck.
Only thing I would add is to make sure as you flip the sail that you get your front hand right up beside the mast - if you dont already do this.
+1 for mast foot pressure. I used to always bounce out of my jybes. Then started using heaps of down force through the boom well before initiating jybe and all the way through it. Really enguages the rail
Bend your knees, keep your arse down, get the board on the rail brace yourself and fully commit. Most important to be full commited !!!
i had the same problem for ages. i found that if i picked a good bit of swell and timed it right, i could be as agressive as i liked without any problems of being bounced off.
same as above though:
bend knees
keep a reach
rear foot on rail, front foot locked in
lay it over on the rail
flick the sail around while still on the swell
youll find the wind will feel like its not there at all until you start pointing a little.
The ever present challenge in cranking hard into the turn is our natural tendency to resist the forces acting upon us. ie. fighting the pull of the sail.
I've see some photos of my gybe when I thought I was really cranking, ie knees really bent, down low and leaning hard into the turn. Well it turns out that the photo proves me wrong! 
. I was just pretending!
Sometimes trying to think too much about the set up makes it worse, for me any way. I'll often try some mind tricks, like looking through the sail to where I need to turn. Or the 'bow & arrow' arm position, ie. front arm straight, back arm pulled back.
I think this photo is a reasonable example of a fast/tight gybe in the surf in strong winds. It highlights knees bent, extra mast foot pressure by pulling down on the boom and an aggressive carve of the downwind rail.
Cheers
^^ If by reasonable example you mean what not to do, then yes. Posts 3 and 4 are the most relevant in this thread, good advice.
If you're not strong enough to pull in the backhand when gybing, then you are going to do a very wide arc turn.
Secret to gybing well in strong wind is to kill the power in the sail by oversheeting.
Using a smaller sail makes it so much easier to oversheet,this is my solution, or find a lull to gybe in.
