Zues writes:
"Surprisingly, the Chinese weren't the only ones who believed there was a rabbit on the Moon, with the Aztecs, all the way across the Pacific, sharing a similar legend."
I don't know if you actually meant the Aztecs, (rather than the Mayans) but there have been more than one historian, archeologist, ethnologist, linguist etc to see an early Chinese influence on the Mayans, most clearly in many similarities between Chinese/Mayan calendars, with eg. the heavenly stems and the earthly branches, and animals associated with them, as well as the bunny in the moon stuff. I once read a fairly extensive treatise on this, which also included similarity in motifs in artwork; also metallurgy. I can't seem to find exactly what I know I read before, owing to the dumbing down of search engine searchs, owing to the overabundance of social media garbage that interposes between information and pages of Twitter garbage. Once was a time when you could actually find important information on the internet.