I found a workaround.
- Export with a white background (or other color that will work with transparent graphics). This will be out "whitescreen" layer.
- Export with "bluescreen" background, or some terrible other color that will make it easy to select out the background from foreground.
- Open the bluescreen version as a layer on top of the white screen.
- Use the bluescreen layer to select out only the parts you want to use.
- Create a mask for the whitescreen layer with the selection made from the bluescreen layer.
This will get good results for edges and aliasing, whilst retaining a good color for the see-