Eöl is (technically) a subject of Thingol, so that does make sense for him to be counted among the Teleri. By having him present at Cuiviénen, we're giving him much more history than appears on the page.
His role in the Episode 3 script is to be an unpleasant loner. He does not have to be affiliated with anyone. But by putting him in the Noldor camp, he's present in the debate from the beginning (since the Great Debate starts out as a Noldor debate before the Teleri and Vanyar arrive). It's a very small detail, and having him arrive later is not a problem.
One thing isn't completely clear to me: at this point, where Finwe is wed, are they still at Cuivienen or already on the Road or already near or in Beleriand?
Morwe and Nurwen still confuse me, I have understood that they are not meant to be the two Avari leaders from PoME but entirely different characters, however still weird that Morwe had interests in Miriel (that destiny thing i already mentioned, though you assured me that Nurwen and Elwe are "just friends").
Considering Eöl, in the PubSil he's a Teler but as far as I can remember Tolkien changed his concepts over the time... at first I think he was an Avar, then a Teler and finally he discussed him eventually having been a Tatyarin-Avar (means one of the Avari-Host that was clo0sely akin to the Noldor, hence his smithing Skills and friendship to dwarves all of which sound more like a Noldo than a Sinda).
We are making Eol Avari without specifying whether he is from the Noldo-group or Teleri-group, at present.
The wedding of Finwë and Míriel takes place at Cuivienen before the Great Debate of whether to stay or go. The Ambassadors have returned from Valinor and invited everyone to go with them, then the wedding, then the but-we-don't-want-to-go voices require a debate to decide the idea. They leave to start out on the road at the end of this Episode.