Unfortunately, it would only get you down ~10^-8, which is still 5 orders of magnitude off (38-8=30>25). Earth is ~12,700km diameter while the Sun is ~690,000k

Unfortunately, it would only get you down ~10^-8, which is still 5 orders of magnitude off (38-8=30>25). Earth is ~12,700km diameter while the Sun is ~690,000km or a ratio of ~50x. The Sun appears as ~0.5deg from here so the Earth should be ~0.01deg from there. A steradian is ~3300deg^2 so we're looking at ~3*10^-8 steradians subtended by earth and roughly that fraction of total neutrinos. Closer, but no cigar.