Greek stress could be used in the medieval period.
Per An Introduction to the Study of Medieval Latin Versification, by Dag Norberg, translated by Grant C. Roti and Jacqueline de La Chappelle Skulby:
in the versification of the Middle Ages [...] the Greek accentuation since the end of antiquity had in a certain number of cases supplanted the Latin accentuation previously in use. In keeping with the Greek accentuation, St. Paulinus of Nola writes aby̆ssus; Fortunatus, emblĕma and problĕma; Aldhelm, machĕra and papĭrus. In the same way in both the metrical and rhythmic poetry we have the early appearance of éremus, ídolum, parádisus, spéleum, trópeum, báptismus, thésaurus, and sarcofágus. According to Lupus of Ferrières, blásphemus is a more correct pronunciation than blasphémus; Gottschalk of Orbais says in his grammatical work that ábyssus, báptisma, bútyrus, rómphea, among others, must be accented on the antepenult, even though the penult is long. In this group must be placed the Greek derivatives in -ία: sophia, philosophia, melodia, theoria, and so on, which in the Middle Ages ordinarily have a long i with an accent on the penult, even though examples of the classical accentuation and prosodic use of all of these words are by no means lacking.62
The prosodic treatment of proper nouns should also be the subject of special studies. [...] Greek proper nouns have often been accented following their Greek accent. Fortunatus scans, for example, Euphemīa (Εὐφημία), Paulinus of Aquileia accents Alexándria (Ἀλεξάνδεια)63, and others provide examples of accentuations of Árrius, Theódorus, Isídorus, Ágatha, Christophórus, Aégyptus, Antióchia.64
("Prosody and Accentuation" page 12)
[Note: I'm not sure why Ágatha and Christophórus are supposed to be telling of Greek influence: Wiktionary indicates final stress in Greek for Ἀγαθή and antepenult stress for Χριστόφορος. Also, I cannot find a Greek proper noun corresponding to Árrius.]
Italian seems to fairly consistently stress learned -ia words taken from Greek on the penult (e.g. teologia) and I'd be inclined to use that accentuation in Latin when using what is called the "Ecclesiastical" mode of pronunciation (that is, the pronunciation system that uses the Italian rules for pronouncing soft c, g as [tʃ], [dʒ] and has vowel length conditioned by stress rather than as an independently contrastive feature).