While attempting to find historical variants of the word in other areas of Japan, I happened to stumble upon the word fabiro "lettuce" in the 1603 Nippo Jisho, which can be found under the form はびろ【葉広】 habiro in some modern dictionaries. This form is interesting because it implies that the word originates from a compound of "leaf" and "wide", which isn't farfetched when you consider that the leaves of lettuce are fairly broad.
Now, while this has nothing to do with butterflies directly, it does suggest that the word はびろ【羽広】 habiro, literally "broad wings", would have once also been permissible. And, as it turns out, 羽広 habiro is used as a placename in Toyama Prefecture and Akita Prefecture. It's also attested as a surname with the readings habiro and hahiro.
So if the word goes back to Proto-Japonic *pa+piro, it's not a far stretch for the word to have become *papero/paperu in early Ryukyuan, and for it to acquire the meaning of "butterfly". If this is the case, however, it begs another question: Is the Japanese word hiiru "silkworm moth", which goes back to *pipiru, related or is it a coincidence? It's difficult to know for sure, but given that the forms heiru and heirume (*pepiru) have been recorded in the Hachijo Islands, I would be inclined to say yes.
All this said, there exists the possibility that this etymology is wrong and that the word may simply be of onomatopoeic origin, especially since so many unrelated languages have similar forms. However, consider this: in Korean, the word 나비 nabi "butterfly" is said to stem from the root *nAp meaning "flat, wide". This would lend credit to relationship between butterflies and the concept of broadness. When making a map of the word butterfly throughout Japan , I also came to the conclusion that the sound or morpheme *pira (hira, hera, hiru, etc.) was very recurrent and seemed to point to ひら【平】 hira "broad, flat", which may be etymologically related to ひろ【広】 hiro "broad, wide". The last piece of evidence is that the Ryukyuan form exhibits voicing of the second /p/ in most of the Ryukyus, which further suggests that *pa and *pero/peru are separate morphemes.
Considering all this, the idea that the Ryukyuan word *paperu/papero "butterfly" comes from the form 羽広 *pa+piro "broad wings" does have some merit. I would be curious to know if the word is used in other dialects and what meanings it acquired in those areas, or if there are other attestations of its use in historical texts.
Food for thought.