This used to be a real problem for me, but I (more or less) solved it in two ways. If you concentrate, you can actually stop too much saliva from building in your mouth and then going into the sax and reed. The big build up seems to be in the neck and reed which effects performance. Also, I swab the sax and neck out three (count em, three) times after every half hour of playing. I use Music Medic sax and neck swabs. That may sound like a lot of work but it only takes two minutes. I hope this helps. Oh, and I have a lint free pad drying cloth and a lint free "shove it".
Kent