The linked page includes a link to the following PDF, which includes some relevant content on page 127 (per the PDF pagination; page 107 as indicated by the page numbers at the bottom of each page). If I've structured the link correctly, it should open directly to the right page, with the content we want in Table 5.1: Examples of bilabial stop in word initial position in the Korean source.
Notably, this table is in Chapter 5. Reconstruction Based on the Korean Source, section 5.1. Consonants, so we must look elsewhere for clarity on their vowel notation. That comes in the following section 5.2. Vowels.
Section 5.2.3.1 Mid central vowel contains Table 5.34: Examples of mid central vowel in the Korean source, on page 143 in the PDF, explains their interpretation of the hangul attestations of Ryukyuan /e/. All of these examples are shown with the Korean vowel jamo of either ㅕ(yeo) or ㅖ(ye), transcribed as jə for the former and jəj for the latter. None of these include the hangul diphthong ㅢ(ui) -- for that, we have to look further down.
Section 5.2.4 Diphthongs includes Table 5.39: Examples of diphthong ㅢɨi in the Korean source, which also includes our peru term.
The key is in the descriptive text below the table:
The diphthong in Table 5.39 should be used for mid front vowel in Old Okinawan. In the word 'rice', 고믜ko.mɨi has a variance 고몌ko.mjəj, indicating that the hangeulㅢɨi is equivalent to the hangeulㅖjəj. If the hangeul, ㅢɨi and ㅖjəj, are interchangeable, and I have reconstructed ㅖ(ye)jəj as /e/ for Old Okinawan, then the hangeulㅢɨi should be also used for mid front vowel. Hence, I treat the hangeulㅢɨi in the Korean source as a mid front vowel /e/ for Old Okinawan.
There are a couple issues that this brings up.
Earlier in the Consonants section, the author explores the details of the Korean source choosing to use aspirated ㅍ(p) word-initially almost uniformly, as compared to using unaspirated ㅂ(b) word-medially. It is clear from this section that the Korean transcribers were being quite deliberate and specific in their spellings when transcribing Okinawan speech. I see no reason to assume that the Korean transcribers were suddenly lax in using ㅢ(ui) and ㅖ(ye), and I cannot agree with the author's contention that these two are interchangeable and represent the same vowel.
Table 5.39 lists six Japonic terms that were recorded using this hangul diphthong ㅢ(ui).
Three of these are known to be terms with 被覆形・露出形 vowel alternation on the final -e vowel in historical Japanese: sake "wine", kaⁿtse "wind" (kaze for our purposes), ame "rain". For sake and ame, we know that the second vowel in Old Japanese was recorded as ⟨e₂⟩.
Kome "rice" has no such vowel alternation, but it too is recorded with the vowel ⟨e₂⟩. → The variant hangul spellings may simply record allophonic forms in different phonological circumstances. The author themselves suggests that this might be the underlying reason behind the different hangul spellings of ⟨p⟩.
We also have reconstructed peru "garlic", which is known in OJP sources to have been rendered as ⟨pi₁ru⟩: the PDF even has a footnote mentioning this and citing Pellard's 2012 work. Per the NKD entry here at Kotobank, it's cited in the Kojiki with the spelling 比流(pi₁ru), and where it's spelled phonetically in the MYS, it's consistently spelled with 比⟨pi₁⟩.
The outlier is are "that". We have no 甲・乙 distinction recorded for the /r/ kana, nor do we have any 被覆・露出 variants.
→ I strongly suspect that the actual phonetic realization of this vowel sound in spoken Okinawan of that time was not a straightforward /e/ vowel, and that this was in fact some kind of diphthong, which only later collapsed into /e/.
The author at no point claims that the hangul string 픠루 should itself be romanized as peru, and indeed they are consistent in listing a distinct Phongram(s) column showing the actual sound values of the hangul. Equating 픠루(puiru, author's strict transcription pʰɨi.ru) with peru is the author's own extrapolation, not anything borne out by the hangul spelling itself.
Taking all of this together, I cannot support any romanization of attested hangul spelling 픠루 as peru: this is just not consistent with known Korean orthography. I would support adding a footnote, ideally quoting the section I quoted above and pointing the interested reader to the relevant PDF. ‑‑ Eiríkr Útlendi │Tala við mig19:29, 17 April 2023 (UTC)Reply
