I like your wavy line idea and starting from the middle and working your way out is good too. I would actually start near the middle for each line and stitch out to the end, then after all the lines are done going one way, turn it around and pick up those lines and go the other way. You'll have some lose threads to deal with, but this method will assure that you don't end up askew when you're done.
May I suggest that if you need to take up some puffy areas and you are a beginner DMS quilter, like myself, you might consider "embellishing" those wavy lines my turning them into a wood grain, or elongated leaf pattern. It's really easy to do, it will help you take up that extra pufffiness and it looks super professional. I'll see if I can post a picture for you.
~ Cindy