Ok, all systems go.
So the first option involves using the medial-axis operation. You could load the image as a raster-layer and then use the expand/contract function in raster-edit mode to beef it up (disable the "Expand Vertically" toggle on there to keep everything at the same height). Then invert the layer and generate your medial-axis carve off of that. You might need to raise the background Z height of the layer to the top of the canvas, if the canvas is larger than the raster-layer, otherwise the edges of the layer will have cutpaths generated off them as well. This method requires manipulating the medial-axis operation via the cutter's geometry. You could just tell it to generate with V-bit geometry but actually use a different bit, like a ball-nose cutter or flat endmill.
Alternatively, you could trace the raster-layer to a paths-layer with a bit of a contouring offset so that the inner/outer paths generated are spaced a bit, and it will also resolve any little gaps there might be in the input image. Then you can use the Shapes From Paths with the paths-layer selected, or individual paths in the paths-layer selected while in path editing mode, to generate a flat shape, basically extruding the paths. You can profile off of these using the profiling operation then.
Here's an example project I just made for you to check out: