https://en.wikipedia.org/wiki/Homestake_experiment#Methodolo...
The Super-Kamiokande has photomultipliers staring at a bunch of water looking for Cherenkov radiation resulting from neutrino interactions
https://en.wikipedia.org/wiki/Super-Kamiokande
None of these are much of a practical option with the moon.
So to place a detector in orbit we'd need one of two things. Space travel to become cheap enough where putting a massive body up is cost feasible, or a radically different understanding of how to detect neutrinos. (First is more likely)
The former also comes with some problems. You'll find more about this by asking why detectors are so far underground. And there's a big connection there to generating the resolution you'd need to map the interior of the Earth.
Then again, it would look spectacular in the sky!
Also, just keep the orbit above 800km, and the light sail will still be able to counteract its own drag.
If the orbit gets too low, turn the ice into rocket fuel and use it to refuel ships boosting into higher orbits.