My less-than-elegant workaround:
Create a rectangle the size of your artboard, then hide the layer to use as your cropping guide.
1. Right-click artboard you want to export
2. Duplicate Artboard to a new file
3. Right-click artboard in new file > Delete Artboard
You'll be prompted to delete the artboard. Select Artboard Only.
4. Now make the cropping guide layer visible and Ctrl/Cmd+click the layer to select the guide, then select Image > Crop
I really wish that was prettier, but it worked for me! If you find a better solution, please reply.