I was browsing through JSTOR when I came across an article (On the Byzantine Greek Pronunciation of the Tenth Century, as Illustrated by a Manuscript in the Bodleian Library, James Hadley) regarding a fragment of the Greek New Testament written in Anglo-Saxon orthography; among other curiosities, the author used the Roman letters “i” and “e” quite interchangably for representing Greek eta.
It appears, then, that in this manuscript we have caught the letter in a state of transition; it was on its way from the ancient to the modern sound; it had become closer than the first, but was not yet so close as the second. It can not have differed very widely from the final sound of English they, prey, convey, etc., which is certainly closer than Anglo- Saxon e, and has in fact a vanishing sound like Anglo-Saxon i. The difficulty which puzzled our writer may be illustrated by taking the three English words ell, ail, eel. The Anglo- Saxon e was like the vowel sound of ell; the Anglo-Saxoni like the vowel sound of eel. For the vowel sound of ail he had no equivalent in his language; how was he to represent it ? If he writes an e, the word will sound ell, not ail; if he writes anl i, it will sound eel, not ail. No wonder that he vacillates between the two, unsatisfied with either. I suspect the η, as he found, it was a little closer than our a in ail; if not, I think he would more generally have used his e.
Here Hadley seems to suggest that η was a diphthong similar to English “they”, I find this interesting. Is there evidence from elsewhere to support this idea? Everywhere else online I’ve read seems to say that η had changed to /i/ by the middle of the 1st millenium although there’s a slight note on wikipedia’s page on Koine phonology that says Cappadocian Greek seemed to occasionally preserve a /ε/ sound. (And actually, the article on Pontic Greek states outright that Pontic Greek preserved both η and ω as pure vowels).
Is it possible that this sound was preserved in Eastern Greek, including the speech of Byzantium, while the Greeks in Hellas itself pronounced η as /i/? This raises another question for me, after establishment of a Greek state after the war of independence in the 19th century and later on after the “population exchange” in the 20th century, how much influence did Eastern Greek have on the creation of the Modern standard Greek language?
Oh, and the article also cites examples of the Anglo-Saxon author transcribing succesive aspirated stops as an unaspirated stop followed by an aspirated one (pth instead of phth, cth instead of chth), I recall annis once mentioning that he didn’t think that Greek had two successive aspirated stops 
; the author also consistently transcribes θ as the digraph “th” rather than Anglo-Saxon þorn, but this might perhaps be attributed to the Roman custom.
EDIT
Has the use of the quote tag changed since the previous version?
I tried typing
to no effect.