Mouthiness is a weekly topic in Puppy Kindergarten. Every week, someone brings it up. Every week, the class is reminded that we have puppies and that puppies are mouthy.
Yesterday, in puppy class we talked about mouthiness with regards to handling. One of the things we were asked to do as part of our homework was to observe how puppies react to touch. Some dogs are calmed by touch where other dogs are aroused by touch. For some just stroking them calmly gets them excited and wound up and that is when the mouthing starts.
We spent a large part of the class working on handling. We would get a food bank in one hand and then touch the puppy with the other hand. This process helped not only to help get the puppies used to being touched all over but also to help them to be calm when being touched. You can use the food to get the puppy in a down while being stroked so it is being rewarded not only for being touched but also for being in a down.
You don't have to just feed your puppy its meals out of a bowl. You can use their meal times to work on calm behavior and rewarding calm behaviors.