Right, this project can't do the Wanderings of Hurin justice by just cramming them into the last episode of the Turin season. They would have to be part of the next season. (For anyone who hasn't read the Wanderings of Hurin, I encourage you to. It's far, for more interesting, and much longer, than the few paragraphs added to Turin's tale in the 1977 book.) As for climaxes, the death of Thingol is already going to be competing with the Second Kinslaying for the climax spot of that season. (Unless Thingol dies in a super boring and silly way, like slipping in the bathtub. )The climax of the Turin story is the slaying of Glaurung. Even if we stretch that episode to two hours (which I think we might have to) that doesn't leave Hurin a lot of time to go wandering around having adventures of his own. Even the story as told in the book we are using as the primary source for this project would stretch the limits of denouement. Now, you could have this be part of the following season, but doing so makes the death of Thingol the logical climax of that season, rather than the 2nd kinslaying. I think that will be a tough sell.
It likely won't prevent it, no, but it will make it awkward and not work as well to chop out part of that story JRR Tolkien wrote.Finally, I don't think that having the Nauglamir made now actually prevents the "Wanderings of Hurin" from being told.
As for the Dwarves not knowing about the Ban... well, why wouldn't they? It isn't something secret, it was a royal decree and probably will be talked about openly among the Sindar after it happens (along with the Kinslaying). I don't see a reason for the Sindar to conceal this from the Dwarves. Indeed, they may warn their allies against dealing much with those murderous, red-handed, untrustworthy Feanorians.
Testing Finrod's attachment to Thingol is an interesting idea, and I think you're on the right track that he wouldn't want to tell the Dwarves he can't use their gift... but they won't ever see him wearing it, and neither will the audience. He'll put it away somewhere, and the audience won't be reminded of its existence until suddely it pops back up several seasons later.
Ultimately, I would like to see this adaptation use the author's actual original intent, instead of the somewhat awkward work-around in the 1977 Silmarillion. There's no need to avoid telling the Wanderings of Hurin in SilmFilm, nor do I see any need to compress such an interesting story until it makes no sense. And that leaves no need to alter the origin of the Nauglamir.