pronunciation - Why does "stigmata" [often] have penult stress?

I have been studying the pronunciation of Greek-derived words in English, and I've found an odd anomaly. There are (at least) two possible pronunciation patterns for plural word-forms that end in -⁠mata (which correspond to singular word-forms that end in -⁠ma).

Antepenult stress (expected)

It appears that it is always possible to place the stress on the antepenult (third-to-last) syllable, such as:

This is what would be expected from the stress rules of Latin (I believe most or all of these words came through Latin before entering English), since the penultimate "a" in the original Greek words is short.

Maybe Latin vowel quality and stress rules are not very relevant; certainly, few English speakers know about them nowadays. And even with antepenult stress, some of these pronunciations do not seem to follow all of the traditional rules for pronouncing Latin-derived terms in English. I was reminded by some comments in this Languagehat blog post that in antepenult stressed syllables, we would expect tense ("long") vowels to be shortened due to trisyllabic laxing (TSL), yielding pronunciations like /ˌtɛrəˈtɒmətə/ (which I just noticed is in fact listed in the Oxford English dictionary) and ?/ˈskɛmətə/ (which is not). (Compare to genus~genera /dʒiːnəs/~/dʒɛnərə/, and perhaps opus~opera /oʊpəs/~/ɒpərə/). However, there are other Latinate plural forms that typically don't have trisyllabic laxing (matrices, also I think helices), or where both the lax- and tense-voweled pronunciations coexist (codices, apices), so I guess the apparent lack of it in schemata should not be surprising. (There are even some exceptions to TSL in singular nouns like obesity.)

Penult stress (unexpected)

The other pronunciation seems to exist only for a couple of words, in which the penultimate "a" is commonly stressed and broadened: stigma ~ stigmáta /stɪgˈmɑˑtɐ/ (listed by both the Merriam-Webster dictionary and the Oxford Learner's Dictionaries), and also sometimes schéma ~ schemáta /skiːˈmɑːtə/ (listed only by the Oxford Learner's Dictionaries). (Neither the Merriam-Webster dictionary nor the Oxford Learner's Dictionaries list *"lemmáta"). I'm wondering why this pronunciation exists. It's an irregular plural either way, and putting the stress on the penultimate syllable creates a stress change between the singular and the plural forms.

(It's true that all of these words are rare, and some people might pronounce some of their plurals differently. The pronunciations I give here are simply the ones listed in dictionaries.)

The plural form "stigmata" is probably most common in religious or theological contexts (where it refers to the wounds of Christ), so at first I wondered if the penultimate stress was supposed to be closer to the original Greek pronunciation, but according to Wiktionary, the stress is on the antepenult in Greek as well.

So, what's up with this? Did the stress perhaps change in Latin over time, is this a tradition of Greek accentuation that I'm not familiar with, is this a simple matter of ignorance of the original position of the stress that has now become entrenched with time and usage, or is this somehow explainable by established English stress patterns? (For example, do English speakers have some natural preference for a penultimate stress on polysyllabic words?)

If nobody knows of a reason, I suppose I can just put it down to people encountering the word mainly in text, not knowing which syllable to stress, and choosing the penult because it sounds better to them.

(I asked this question a while back on Wordreference, but nobody knew of any reason.)