Regarding the conceptual problem of determining whether what we speak of as a translation of a poem might not be more precisely thought of as a new poem perhaps based on or inspired by the other one in the different language - or the problem of what we really mean when we call call the one text a translation of the other - I must think of the vagueness of language and the near inevitability of borderline cases that come between the clear prototypes of so many concepts. The classical example are concepts like 'tall' - Labron James is tall; Mickey Rooney was short. But between these clear cases there are borderline cases, and no clear non-arbitrary line to be drawn that will determine when someone starts or stops being tall.
The same seems to be the case here with 'translation': 'my cup in on my desk' seems to be equivalent to, even synonymous with, 'meine Tasse steht auf dem Schreibtisch' - they express the same proposition or have the same meaning. Just a 'cup' seems a synonym of 'Tasse': in any sentence, to say 'cup' in English is just to say 'Tasse' in German; two words expressing the same concept. And 'Buch' (book) would clearly not be a translation of 'cup': those two words express different concepts. So a clear case of non-translation. Your poetry example contains propositions and concepts that can be translated with synonyms; others that can be translated only by different from overlapping concepts and propositions - as spirit in English and Geist in German have both differences and similarities: to don’t express the same, but analogous concepts. If the analogy in a particular use is strong, then we can also speak of a 'good translation', and if not, then not. But already that means something different than translation-as-synonymy or strict equivalence. Perhaps in some instances, you might find some that are not even translatable with analogical concepts (Geist and spirit are analogical in that they express similarities and differences). A strong analogy would be here: given the meaning-in-context, which provides the criterion of relevance, the similarities are highlighted and the differences recede to the background.
The 'feeling' of a poem is largely a function of the form and the sound (music). A limerick produces a certain effect in English; a German translation of the limerick would thus have to produce the same or an analogous effect, and thus either translate the verse form entirely or find a German equivalent that produced the same set of possible intelligible effects. So would add that to theory/hypothesis.
Same with sounds: hard sounds in German (k, ch,
etc) and certain meters correspond (like different kinds of music) to different
emotional states - equivalents or analogs to sound and rhythm would thus have
to be found.
So my hypothesis would be:
For all poetic texts, a rendition of, say, German language text G into English poetic language text E is a translation of G into E only to the extent that the propositions and concepts expressed in G are rendered with the synonymous or relatively strongly analogous concepts and propositions in E, and the poetic form in G is rendered in E in such as way so as to produce the same possible set of synonymous or relatively strongly analogous emotional effects in the readers of E as those of the readers of G, and the sound and rhythm of G is rendered by sounds in E so as to evoke the same or similar emotional atmosphere.