I can tell you from experience that wet mouth is a very hard habit to break. I'm very big on improvisation, so I am used to all types of things happening during a live performace. In one case, (I was around 12 when this happened), I was the featured saxophone player in a convention concert. I had to improvise in my fillers, but halfway through the concert, my saxophone starts getting a disgusting tone to it. I realized that it was because the reed was getting wetter than it should be. I had to be quick and undo my mouthpiece, polish the reed, and redo the mouthpiece before the solo began... I've never felt so nervous in my life! But I found that a way to break the habit is to try to not drink a lot of water before a performance. This worked for me, but I still had recurring "wet mouth" situations.
A couple of years ago, I found that there is a reed that is very resistant to moisture buildup, and tone deformation. The first time I tried out the "Plasticover" reed, I immediately loved it! Try out the plasticover reeds, and give me your opinion on it. Some people say that there are different kinds, but the only ones I've seen are black, have a slight purple "gloss" when they're new, and have a brighter tone than the wooden reeds. I now use nothing but plasticover reeds when I give performances, and they have never failed me. Actually, I only had to replace the reeds after about a month each. They are very break- resistant!
So, I hope that this info will help you take care of your wet mouth problem. Remember, you are not alone in this situation!