I'm trying to make a puzzle using Inkscape to be cut in a Glowforge. My plan is to engrave the back, then engrave and cut the front.

I thought I did the art correctly, blue lines for engraving and red lines for cutting. black lines are registration. The finished art is here: https://inkscape.org/~Mjphil/resources/

The problem is that the Glowforge sees ALL the paths I drew, including the ones I stroked white, or covered over with a new layer of white. You can see this by opening one up in Inkscape, and looking at it using "View-Display Mode-outline"

Is there a way to prepare a file that only has the blue and red line visible when imported into Glowforge?