I completely disagree that a white tongue always or nearly always means you have thrush! In Chinese medicine a white tongue can mean many different things. Quite often it signifies "internal dampness," which might not even cause bowel problems and so on. As Jhan said it is generally said to reflect the colon/bowels- which is odd if you are that regular.
You could look up a white tongue in Chinese medicine or ayurveda and look from there. My white tongue has cleared up from drinking kombucha and kefir. But recently I went camping with a couple of friends, all of whom were drinking a lot and admitted they hadn't had a BM in the few days we were camping- and hey presto, all had completely white tongues. Maybe it was because their colons were backed up. Maybe it was just all the booze. Try some homemade probiotic drinks (kombucha, kefir) and see if you notice a difference! I have a lot more saliva and no more icky taste in my mouth or sore throat any more after starting them.