If it were me, I would send them out to the person you know can finish them and let the conseqences play out. If the first woman believes that the world should stop because she had surgery, I wouldn't place a lot of value on her friendship.
However, if it's important for you to stay in her good graces for some reason, I would call her and offer her the chance to quilt your tops with the deadline that must be met. If she turns them down because she can't physically do it, then you can take them to the other person with a clear conscience.