Sounds like a great project!
270mm FL is a fair dispersion for a SA grating, so you'll need a couple of frames to fit it in and a longer exposure, guessing 3 -4 sec.
You may want to make a set up like Samir has on his webpage (
www.samirkharusi.net/spectrograph.html) to at least get the arrangement working. I use a cardboard box 1200mm long to get focus with my Zuiko 135mm telelens. A Dulux fluro energy saving lamp has some good reference lines for calibration. Could be easily adapted to use the needle slit.
Keep up the good work!