Certainly a good start. What are you using as a stencil emulsion? and are you coating it both sides of the mesh?
If I were doing this I would try to increase the stencil emulsion thickness rather than go for a coarser mesh which may leave marks.
EDIT: Thinking about this, you are probably not using anything as a stencil emulsion as you are just printing a rectangle. In which case, I would experiment with masking off the area with increasing thickness of tape.