Hi ZRaffleticket,
thanks for sharing your discoveries with us. The pattern you see looks more like a broader emission spectrum, than a one that consists of multiple lines.
Usually the emission width (FWHM) of a GaN laser diode in the + 450nm region is around 2nm. The width of the gain profile though is around 10nm, so
in general every frequency in these area can lase if it has enough gain. Your pictures look for me more broadened than two distinct lines (the human eye
detects light with a logarithmic scale, so it is hard to tell without a camera or s.e. similar if the brightness is half as strong or just a few %..)
Have you moved your grating (without changing the angle in respect to the laser beam) to cancel out spatial deformations of grating? A measurement
with a spectrometer can resolve your question but also a picture of a direct caparison with a laser diode, that you know is operating in a single mode
would help.
Singlemode