If they make a darning/free motion foot shouldn't they make a darning plate for the same machine? A darning plate covers the feed dogs instead of them dropping. I have a cheap brother and the feed dogs do not lower but I have free motioned MANY things in the past I just cover them with the darning plate and attach my darning/free motion foot and go to town!
OR I have read that you can also lower the stitch length to 0 and they won't move, attach your quilting foot and try it that way. I have never done it this way but if I were you I would practice it this way before doing it on your quilt!