Good transliterating. Honestly, as I said, I am not fussed about breaking the rhyming scheme, I think it still works and it doesn't jar, and even the meter might be worked in somehow. But for thoroughness sake, going by stanzas, and (hopefully) marking all the jarring deviations from meter (because several lines technically don't match perfectly but still scan fine). I'm bolding the stanzas with the rhyme change, but meh, if they don't follow the pattern it's not a loss. The meter is the more challenging thing.
Speak... turning to thee
FINROD:
ABC
AMARIE:
ABC - "undying" sticks out by a syllable, which is a real bummer because I like it.
Listen... ignore how you ache
FINROD: ABC - can we cut "A"? If not, it can stay as a hanging syllable.
AMARIE: ABC
Look though... scream through the Night
FINROD: AB - "chasms of ice" wants more syllables... not sure how many, doesn't have to match exactly. One or two would work. There is just space which seems to need filling after "over". Maybe stick an adjective in there?
AMARIE: AB
Feel... like a gate
FINROD: ABC
AMARIE: ABC
Heed me... barred gate
AMARIE: ABC
BBC - "pathways of fate" is missing a syllable, but could be sung as "fa-ate".
Answer...turning to thee
AMARIE/FINROD/BOTH: ABC ABC - could stick an extra syllable in the first line but don't have to (eg "now/for I am turning to thee"); optional.
So yeah, not that many places. And of these, I think "undying" is probably most awkward. I haven't sketched it yet but I will try to play with the music to make it less jarring, because I really like that stanza by content.