I have any number of screwups like your cutting board. It’s the reason we have that feature. You’re not alone. 
So there’s a few things you can do.
For bitmaps, you can engrave them.
For vectors, you can engrave them, as you might for text. You can cut them, as you might for a shape. You can hairline-engrave them, which is like cutting but at lower power, so you trace the outside.
If you look at the macbook skin on the glowforge homepage, you’ll see the logo over the center was cut, and the lines were hairline-engraved, and the text is a vector that was fill-engraved.