are you using a template with either a no melt plastic or other template material to turn your edges over. Perfect Shape from The Stencil Co or Templar (ususlly found in shops) is a method to turn edges and press them down. This gives a nice crisp edge. There is also a method using freezer paper or a pellon type material. This is good to use whether you do by hand or machine.
Also, straight stitch or raw edge, to me, would be out of character of the ret of the Dear Jane quilt as the style is mide 1800's.