I have a Janome 6500, about 10 yrs old, and I free motion quilt without dropping the feed dogs. It calls for dropping them but it works many times better not to drop it. You might want to try it on your machine.
If you still want the feed dogs out of the way you can tape an old credit card over it or for some machines you can buy a small plastic cover you snap in place or it comes with the machine, like Janome Jem silver 3/4 machine.