No, I'm not doing the "leave it alone" method. The past almost 3 months I was using Protopic once per night, and another cream during the day. I did very gently wash off the build up after about 7-10 days during that time.
Before using anything on my lips, I could even wash my lips with water twice a day (I used to use qtips with salt water) without too much build up coming off. Now when I started using moisturizers, the build up is easily washed away with water, which is why I stopped getting them wet. You can see a picture in the Image Gallery of how easy the the skin comes off. In that picture, all I was doing is let a bit of water run over my lips, basically.
Once I start doing the moist healing treatment (some time after my vacation in the US), I might try getting them wet more often. But I'll still brush my teeth and get rid of the toothpaste the way I'm doing it now, I don't think getting toothpaste on the lips will help. :-)