What bluenose says is right. You don't really need more than 7-8 feet of overall leader on the UC for Brookies in most situations. In the wind it'd help alot. You could stay with 5X as well and that would help the fly to turn over better in those conditions.
A plus is the shorter rig will catch fewer tree fish also !

Fred

Buzzy, the 9.5ft leader is fine but the 2 feet of butt and the 2 feet of tippet bring the total leader to 13.5 feet.  Couple that with the windy conditions and it would be hard to hit a hoola hoop.
Either shorten the leader (use a 9ft 6X and loose the 2 feet of butt) or tilt the trajectory of your cast slightly forward with a shorter stroke.  Stop your backcast at 12:00 (straight up) and take the fwd cast to 10.  That will result in a tigher loop and a downward trajectory.  Keep cast in that kind of wind as short and low as possible.
Cheers

I agree with siestafred. Using a 5x is probably a better bet than the 6x. I've found that I've had no problem whatsoever catching fish on the 5x when normally you would use a 6x, so now I rarely use anything smaller than the 5x and the turnover on the fly is much better.

I've been playing around with the same kind of fishing out here lately. Some BWO dry fly action coupled with a lovely western style breeze is always interesting.

For a lot of dry fly fishing I do use a longer leader as well; somewhere in the 11' - 13' range a lot of the time. The main thing with the longer leader is that coupled with a slack cast it can allow you to drop your fly in a little pocket/slot of water with a different current than the water the leader lands on. With a longer length of light tippet the leader takes longer to pull up the slack and the fly hopefully stays in the zone longer. A lot of the browns I find around here are feeding along a seam or tight on a bank so the currents are pretty wonky (swirling, or they may be in the protected pillow of water just off the bank, etc) - without the additional length it's very very difficult to get a good drift.

Flityr hit the nail on the head with his response though... Get rid of that additional butt section, shorten or eliminate the tippet, and change the trajectory of your cast. Changing the trajectory on the cast will let you get the fly closer to where you want it, but depending on the wind and the angle of your cast you risk slapping the fly/leader/line down harder than desired. So be mindful of that. Sometimes if you're not sure how it will play out try making a couple practice casts a ways off from the fish so as not to spook but to get a feel for where the fly will land.

Everything outside of ideal conditions requires compromises though, and you need to measure each factor... Say you shorten the tippet up long enough that you can get a more accurate cast but because of the current you can't get a drift then maybe you have to re-look at the tippet length or how you're laying down the leader (i.e. if it lays out completely straight without slack drag can become a problem quick). If the wind is consistent you can adjust your target to the left or right depending on where you see the fly landing; not easy if the wind is gusting though... If you can't see your fly that makes all of this tough too. Picking patterns with a bright post for the wing or something similar is very helpful in determining what is happening.

If the wind makes an accurate drag free drift seemingly impossible, there is usually an option to feed line down to the fish from upstream. Harder to get a hookup but better than getting no eat at all

dan