I think that it was important to Tolkien that characters not just instantly be able to understand one another when speaking different languages. So, the meeting of the Sindar and the Noldor should probably *not* be handled simply with accents differentiating them. HOWEVER, once they've met and mingled and learned each others languages, then the accents would be a good way of showing who is not speaking the language on screen 'natively'.
So, I do like the accent idea, but I don't think it address the overall issue satisfactorily. I want the viewers to know that the Noldor speak Quenya and that the Sindar speak Sindarin, and that the dwarves have their own secret dwarf language that we don't know too much about.
[Orcs can just speak crudely, but if we want to have some Black Speech, well, I suppose we can work that in. Maybe the orcs don't even 'speak' in their earliest incarnations, but are much more beastly?]
In Season 2, there are a few specific things we can do to start introducing the divergent languages idea.
One, when the Teleri do finally arrive in Alqualondë, they can have a few unique words in their own language that the Noldor do not have. Probably relating to ships or the Sea. So, when a Teleri is speaking of these things (in English), we can slip in a Sindarin word that either needs to be explained on screen or subtitled.
If we decide to have Rumil on screen, he can complain about the changes in the language, or explain the need to write stuff down in the context of 'see, even the next generation speaks differently, and now that we are in Valinor, we are forgetting the Great Journey and what we learned then.'
The Shibboleth of Fëanor (don't mess up my Mom's name!!) might not be great on screen. But if Rumil needs someone to argue with....well, Fëanor is available!
But mostly we have the Frame. All of the names - Fëanor, Fingolfin, Galadriel, etc are the SINDARIN names of these characters. Their Quenya names are Fëanáro, Nolofinwë, Alatáriel, etc. I am fairly certain we don't want to use the characters' Quenya names. But we can mention that we are using their names as they were remembered in Middle Earth, in Sindarin, in the Frame. A discussion of 'what is the *true* language of the elves?' should fit the theme we are trying to develop in the Frame.