Thanks again, everyone!
I did end up pulling out the black quilting around the dragon and redid it by hand (I just didn't like the way it looked, I used too big a stitch and didn't maintain good machine control).
I finally built up the courage to wash it this evening, and the dragon stayed put! It did "puff" just the slightest bit due to the shrinkage of the cotton quilt, compared to the non-shrinking dragon, but it's not loose, and didn't puff in a bad way, just gave it a little more 3-D appearance.
I have some other projects I'm working on right now, but I'm positive this won't be my last castle quilt.