You can move the quilt with the needle down. You just have to be very careful when doing so! I have had to do it a few times (I didn't plan ahead LOL). I always make sure the needle is all the way down and roll the take up roller very slowly.
Removing stitches is easier if you loosen the quilt on the rollers just enough to be able to get a little play in the fabric.
Both of these methods seem to work for me.