For the record, it wasn't actually FDO_E_FEATURE_EMPTY_GEOMETRY - error code -2147217383 is also E_RASTER_FAILED_TO_COPY_DATASET (which makes a lot more sense).
Looking at archived forums, I see people were having this problem years back. No answer then, no answer now. In the end, I got around it by saving initially to a BMP file, then used System.Drawing.Image.Save to convert that to JPG.