Well, I've managed to get it working, although somewhat hackily.
It turns out the laser cutter software is expecting a "layer0", and not the "0" that Altium produces. I can leave the "0" layer there and just rename the one I want to "Layer0" and it works, although the scale is waaaayyyyy out for some reason. How do you change between metric and imperial for Camtastic's DXF export?
Dan