not sure how you got to this point, but when you zoom way in you can see this: the double-line ones are the ones that look scored, but are actually a very thin engrave.
your cut line from using the pen in photoshop looks like it worked out fine. If you were gonna stay in photoshop, I would put those cut lines around the original jpg, and engrave it as a raster.
edit-
here is the tutorial I wrote for doing that
in your case, you would use the pen tool for the outline instead of a “shape” tool.
