So, we do need to pass Narsil on prior to Andreth's death, and we will be visiting Brethil in Episode 11 to set that up. The character the sword is passed to needs to be someone the audience already knows, though, because the only 'new' characters from the House of Bëor that we are introducing at that time are possibly Morwen and Rían. While I don't mind Beleth existing among the Bëornian refugees, and I think it would be helpful to have some names Tolkien included on standby to use for any background characters who have lines, I don't think we have any intention to introduce Beleth as a character the audience knows at this time.
For Season 5, we were very judicious about how many named human characters we expected the audience to know and keep track of. For the House of Bëor, that meant: Bëor, Adanel, Andreth, Barahir...with introductions of minor characters Bregolas, Beren, Baragund, Belegund, Gorlim, Emeldir. Other lines were given to background characters like 'old guy' or 'singing youth' - not characters the audience was expected to learn the name of or keep track of.
Andreth and Emeldir have been acting as de facto leaders of the refugees since the Dagor Bragollach. At the time of the evacuation, Andreth was still a 'Wise Woman' of the House of Bëor, and thus has an official leadership position (the stole). She had acceded military leadership to others in Season 5 as a result of the move to Ladros, but retained some level of civic leadership. When the decision to evacuate happened during the sudden flame of the Dagor Bragollach, Emeldir stepped forward and took shared responsibility for that. At that time, she is the wife of the military leader (Barahir), and both she and Andreth are assuring the others that they will get the women, children, and elderly to safety. So, it is the decision of the gathered leaders that Andreth and Emeldir do this.
We have not yet visited Brethil to see the state of the refugees living there. But I see no reason why Andreth and Emeldir would not continue to be the leaders in the years since the battle. It is true that when Beren arrives, he will confirm the deaths of the outlaws (no doubt strongly suspected by this time - it has been years since anyone has heard news from them). So, at that time, Emeldir becomes the wife of the deceased Lord of Ladros, rather than the wife of the current (or presumed dead) Lord of Ladros.
But...there is no more Ladros. The House of Bëor is a people without a land, and will be moving from Brethil to Dor-lómin at the end of this season (Episode 13). So, we don't need a Lord of Ladros after the death of Barahir. Emeldir is the one who makes that decision and leads the people. So, it would make the most sense for her to have the sword - for Andreth to have passed it on to her. Note that Narsil is *not* an heirloom of the House of Bëor. It never belonged to the chieftains or anything like that. Narsil was Aegnor's sword, and is given to Andreth in acknowledgement of her grief at his death. So, it is a personal belonging of Andreth that she may pass on to anyone she pleases. She chooses Emeldir. At this point in time, the only other option is for it to be given to Morwen (Rían is too young). So, if we want it to become Húrin's sword, we could do that.
It is definitely our goal to get Narsil to the Mouths of Sirion, and to have it go to Numenor with a character who is not Elros. As you point out, it needs to become an heirloom among the Faithful, not of the Kings of Númenor. There are a few steps in the middle that we are missing, so one of the questions for Season 7 will be...'who does Emeldir give Narsil to and how does it avoid being left in the Haudh-en-Ndengin at the Nirnaeth Arnoediad?' I know some people have some ideas, but nothing definitive has been decided yet. One option is for it to reach the Havens via Gondolin rather than via Dor-lómin. An earlier idea was to leave it in Brethil until the time of Túrin, but the hand-off to Emeldir seemed more important here and we've since discarded that idea.