Learn English – How to Pronounce “Deictic”

Generally in English the addition of an inflectional ending does not affect stress. That is, the ending itself is not stressed, and stress remains on the same syllable as it is in the uninflected form. For instance, even though in morphologically simple forms, we don't get 3 unstressed syllables at the end of a word in English, the addition of the -ing inflection of the progressive aspect does not affect the stress, even when it is added to a verb ending with 2 unstressed syllables: interest/interesting, amnesty/amnestying.

Likewise, the regular English plural ending is inflectional, and its addition never causes stress to shift to the right, nearer the end of the word: parentage/parentages, Cavendish/Cavendishes.

Therefore, if the -ta is a plural ending and is counted as an inflectional ending, like the regular plural ending, one would predict that stress would be unaffected by adding it, and you would get stigmata ending in 2 unstressed syllables. That is a big "if", though, since I don't think stigmata is actually the plural of stigma in current English, and I never heard it pronounced on anything but the penult. So I think the stress you are asking about is archaic in English.

Looking at words beginning with ortho- there seem to be two possible pronunciations:

/ɔːrˈθɒ-/ as in orthogonal or orthography,
/ˈɔːrθə-/ as in orthodox or orthodontist,

where the second pronunciation has primary or secondary stress on the first syllable.

But in English phonology, the vowel /ɒ/ must be followed by a consonant, so the first pronunciation is ruled out for orthoepy. This is presumably what Walker meant when he said “Orthoëpy, having no consonant in the antepenultimate syllable, naturally throws its accent on the first” (1822).

You could also pronounce orthoepy /ɔːrˈθoʊ.iː.pi/. This seems to be what Robert Nares meant when he said that "the accented vowel is long in the antepenultima" (1782). However, there aren't any other words where ortho- is pronounced this way. I suspect this discouraged people from using it.