We present the latest results from a spectroscopic survey designed to uncover the hidden population of AM Canum Venaticorum (AM CVn) binaries in the photometric database of the Sloan Digital Sky Survey (SDSS). We selected ~2000 candidates based on their photometric colours, a relatively small sample which is expected to contain the majority of all AM CVn binaries in the SDSS (expected to be ~50). We present two new candidate AM CVn binaries discovered using this strategy: SDSS J104325.08+563258.1 and SDSS J173047.59+554518.5. We also present spectra of 29 new cataclysmic variables, 23 DQ white dwarfs and 21 DZ white dwarfs discovered in this survey. The survey is now approximately 70 per cent complete, and the discovery of seven new AM CVn binaries indicates a lower space density than previously predicted. From the essentially complete g~19 sample, we derive an observed space density of (5+/-3)*10^-7^pc^-3^; this is lower than previous estimates by a factor of 3. The sample has been cross-matched with the GALEX All-Sky Imaging Survey database, and with Data Release 9 of the UKIRT (United Kingdom Infrared Telescope) Infrared Deep Sky Survey (UKIDSS). The addition of UV photometry allows new colour cuts to be applied, reducing the size of our sample to ~1100 objects. Optimising our followup should allow us to uncover the remaining AM CVn binaries present in the SDSS, providing the larger homogeneous sample required to more reliably estimate their space density.