I am a rebel. <G> I don't use either a walking foot or a darning foot for quilting. Most of the machine quilting I do I use an open toe applique foot.
The key is to reduce the pressure foot pressure. On older machines there is a "screw with a knob on it" on the top of the machine..... that regulates the pressure of the pressure foot. To see what I mean, put the foot down and lift up on the toes gently. For most sewing you want some lift but not much. If you put two layers of fabric under the foot you shouldn't be able to easily pull it out. If the pressure is tight you really can't lift the foot, as you loosen the pressure it gets easier to lift it. So if you loosen the pressure to where there isn't a lot of "drag" on the foot/ fabric sandwich you will be less likely to have problems. You can loosen the foot quite a bit, sometimes enough that the feed dogs don't actually engage the fabric. <G> But I believe most Featherweights have a plate that screws on to the bed of the machine to cover the feed dogs in order to do free motion work.
Remember that when the Featherweights were state of the art our foremothers were doing a lot of darning, and machines made that a lot easier. <G>
Have fun,
Pati, in Phx