One of the things I was never really happy with in Engadinese was the fact that Greek has a fair number of words with stress on the final syllable—this resulted in a language with a rather different feel from Romansh since all the dropping-unstressed-final-syllable thing didn’t work as pervasively.
Most importantly, a word such as σοφός could not really give σοφ or the like, so I settled on something like σοφό—but then you have masculine/neuter words ending on consonant or stressed omicron, which seemed odd to me. Similarly, contract verbs with their final stress also didn’t act much like non-contract verbs.
So, perhaps something that I could do would be to do a wholesale stress change, to make Greek stress more Latinate, before going on to do sound changes.
That’s not unheard-of; after all, that’s what happened at some point in Proto-Germanic, where the PIE accent turned into a stem-initial stress. And, though I know less about such things, presumably also more or less what happened on the way from Proto-Slavic (with, presumably, variable stress) to Polish with its fixed penultimate stress.
It would also be interesting to see what changes to inflectional morphology (and indeed, to the entire feel of the language) such a stress change would bring about. (For instance, it might be easier to merge final -η with -α if the final syllable is never stressed.)
I think I’d have to study Latin stress a bit more carefully first, in order to get a bellyfeel for it.
Engadinese would, of course, not have no final stress; it would almost certainly acquire it through dropping of formerly-final syllables. (See e.g. Romansh -ziún from -TIÓNEM.)