Warren, it's really exciting to see this sort of technology diffusing out of academia. All of your question are interesting, here are a few more thoughts: 1) Seeing that your baseline is almost half of your maximum signal, I wonder how much attention you've paid to isolating the sensor from external light sources? It can really improve your SNR to be very picky and careful about this--e.g. we would tape aluminum foil over all the windows and then black paper/cloth over that. Or is that baseline really the ccd/cmos thermal background?
2) Extraneous scattering from the laser can be tricky to eliminate as well; a long pass filter just in front of the sensor could help with that. They're not cheap, here's one possibility. 3) Adding multiple image captures of the same spectrum (e.g. in ImageJ) might be a cheap hack in place of, or at least for evaluating the benefit of, longer exposures. 4) By way of lab safety, there is research suggesting that the high energy end of the visible spectrum is energetic enough do damage to your retina; since I tend to be a nerd about lab safety, I might wear a good pair of blue blocker sunglasses while working with this laser. It would be nice if someone really knowledgeable about this could comment.