Besides, I'm certain my numbers are large overestimates. I extrapolated numbers from a completely different scale; surely optimizing for this problem would yield very different designs. Like more focused neutrino beams. They have a large fraction of their neutrino beam going out >6 km off-axis (at 810 km distance); at 8,100 km, this would be >60 km off axis. So there's maybe 6-7 orders of magnitude potential in designing a lower-divergence beam.