I have recently been reading poetry by John Keats and Rabindranath Tagore. Both these poets, being active in the 19th century, by which time I think English was quite as it is today, wrote still in what I guess was Early Modern English, Keats especially, being an admirer of Shakespeare. However, there appear to me, in their poems, mixtures of the two- Early Modern and Modern, in particular as with the endings for third person singular present forms of verbs- for instance, sits or sitteth. Were these choices purely made to accord with the ongoing rhymes? Or is there another reason? In Shakespeare himself, I found on the internet the following: "With her, that hateth thee and hates us all". How come hateth and hates is being used simultaneously?
I sometimes use an earlier work for inspiration and will pay tribute to the original author by skewing the word choice towards their usages--sometimes this is done for comic effect and sometimes to add a few lyrical tones. An example would be Wifred Owen's use of "thee" "thou" and "thy" in his earlier works--most likely as an homage to his influences. See Owen's "To Posey," for a vivid example of him playing homage to Keats, Coleridge, and Tennyson--Keat's influences the structure and tone more than anyone, but some lines refer directly to lines written by Coleridge and Tennyson.
This may not be the case for the poems you are looking at, but I would suggest seeing if there are any correlations between the poem in question and an earlier work(s). Also, reading a few scholarly critiques of the poem should give you insight into what the poet intended, and if there is special significance in the word choice, it should be made more apparent.
My guess is poetic license (use of -eth) and consonance. hateth thee (/th/ in common; although not the same sound, produced in the same position) and hates us (/s/ in common). And he gets an extra syllable for free :)