Chinese cooking troubleshooting: still biting into pieces of ginger
I like using a microplane to very finely grate the ginger (that's easier to do if the ginger is frozen), or making a paste with the ginger in a food processor or blender. Just peel the ginger (you don't have to be perfect), cut it into chunks, add just enough water to get almost a baby food consistency and puree. Then you can stir-fry the puree to flavor the oil, add it to soup, add it to anything that you want, and use as much as you want but you'll never bite into a chunk, nor will you ever need to fish it out of anything. The ginger paste will last quite a while in the fridge and won't suffer a bit by being frozen for up to a year or so. Make the paste with half ginger and half garlic and you've got a great convenient ingredient for all kinds of applications.

EDIT: This question inspired me. I needed a housewarming gift for my new neighbor and landlord. When I freeze ginger/garlic paste for myself I have always just used ice cube trays, but for a gift a little cookie scoop worked great. I just scooped the paste, froze the little rounds on freezer paper, then packed them in Ziplocs.