Which leaves the first option as the more likely of the two if we consider these factors.
I disagree.
If fighting did actually take place between the Apollo 13 astronauts, then Neil Armstrong would have mentioned the lunar rabbits in his after-action report when he came back from the moon, and Erin would have mentioned actual fighting on the moon, instead of "they build some stuff and then left" also, Neil Armstrong and Buzz Aldrin FIGHTING SPACE RABBITS ON THE MOON* would be a pretty major plot point, i think Zun would have talked about it in more detail if that was the case.
So my guess is that ether:
1. Eiki was referencing another conflict that happened in the past, that had nothing to do with Apollo 13, but did involve fighting, that Reisen abandoned.
2. Eiki was making shit up/misunderstand something in reisen's past as a excuse to criticize reisen (i doubt this one is the answer, because if its true then Eiki is almost as dumb as Cirno, which is obviously not true.), or that the Crystal Mirror is NOT as powerful as it seems, and has some limit to its power, like only being able to see the past from the subject's prospective, or something like that.
3. Zun's original idea was that the rabbits did fight the astronauts, but then realized how stupid that would be, so he retconed it, but wrote Phantasmagoria of Flower View before he decided that, and thus Eiki's comments about Reisen are no longer canon. (This is not the only thing Zun has retconed something)
Honestly, the other bits of evidence point to "There was no conflict" too much for there to have been an war between astronauts and moon rabbit, and besides, its unlikely that any of Resien's allies would have died, as no astronauts in history has ever brought weapons to the moon, unlike the rabbits, who probably did, so if there was ever a fight, the Astronauts would have been CRUSHED.
*Its possible that it was one of the later lunar missions that led to a conflict, but my two points that 1. Eirin would have mentioned a actual battle and 2. The astronauts would have mentioned it when they came back** still stand.
**Its possible that, in a true Conspiracy Theory fashion, the US government prevented any news of the aliens from reaching the earth, but that still doesn't explain why Eirin never mentions any actual battles or causalities.
Why is anything related to the moon so damn complicated?