I have been dealing this this "over achieving salivary gland" problem for over 50 years. Please re-read my first post on this topic and do all 3 suggestions, polishing the back of your reed till it is almost shiny enough to see your reflection. I guarantee it will control your problem. I am an expert on this topic and well qualified to give this advice since one of my clarinet instructors in college suggested I get one of those suction hoses dentists use and hang it in the corner of my mouth when I play.
Thanks for the advice, and the good laugh. I do polish the reeds (see above) and try to suck in when I can (mostly to disguise the fact that my stomach is on the rotund side).
Polishing the reeds doesn't seem to have had much effect. But it was partly your post, and another I saw elsewhere that prompted me to ask about synthetic reeds and if they might allow the water to roll off more than cane.
But I will try inhaling harder. Bearing in mind that me and several politicians have never inhaled anything in our lives. I might need to borrow a suction hose.