Yes, we need to be aware of our 16th century (& earlier) roots.
By "rehashing" I mean just repeating old arguments as if 450+ very
eventful years had not passed. Bilateral dialogues between various
pairs of communions have achieved a good deal since ~ 1960 (though I
think the current Lutheran-Reformed proposals paper over important
differences). These dialogues haven't touched much on science-theology
matters, nor would I have expected them too. That's the task of those
concerned with science-theology matters, & that group doesn't overlap
strongly with those focussed on ecumenical affairs.