I think the Lego spectrometer's suitability for this is an open question, but the Raspberry Pi Camera v2 is very low noise and could be worth testing this idea out with. Please post your results if you do!
I have used photographic neutral density filters and have not been able to view the sun directly using the spec3 highly modified device. The attenuation ranged from 2-400 and have added additional attenuation resultong in overexposed images. Do a search of my previous spectra. I have built many versions of the original.
Further to my previous replies, it may be possible to view the sun disk attenuated with the filters used by welders to view their work. I have not as yet tried this idea but do know that these filters are replaceable. Try harrbor freight or some other supply store for these filters. No guarantees that this will work for you, as it would require some form of spectral calibration to see what the response is.