Use of 'outlandish' subplots for the Frame is quite common on some shows.
Angela spends Season 3 of Bones hunting down her husband from a brief marriage in another country, so she can finalize a divorce and get married. The existence of said (ex-) husband was revealed during her attempted second wedding in the finale of Season 2. Her new fiance gets to be totally intimidated when the guy turns up and happens to be extremely physically attractive (and nice/romantic too). They do have more mundane subplots, like office romance and difficulties with raising kids. But they seem to go for 'colorful' backstory when they can. It's the type of show where a new character can ask, "So, what happened to the guy who used to work here before me?" and get this answer: "He joined forces with a serial killer who was the last in a long line of cannibalistic murderers specializing in knocking off members of secret societies and building skeletons out of their body parts."
On House, Thirteen is super-secretive about her personal life. It is eventually revealed that her mother died of Huntington's, and she's afraid to test herself for it. She euthanized her brother when he was dying of it, but no one could prove it. So House obtains a blood sample from her using dubious methods and gets the test done himself. Once she realizes that her boss knows and she doesn't, she looks at the diagnosis - she has the disease. When she gets into an experimental drug test to help prevent onset of symptoms, her bf meddles with the test to make sure she's not in the control group. These are 'medical' subplots, but rather out there. [And then there's the subplot where House takes way too much Vicodin and starts hallucinating a dead intern.]
So, on one level, the audience might not be surprised if we introduce a character who just happens to be well travelled and know everyone in Middle Earth - she's friends with Círdan...and Treebeard...and Radagast! And can make jokes about who is older (she is, obviously). Every Tolkien fan watching the show will accuse us of introducing a Mary Sue, but whatever. But the *only* thing we need this character to do is a) have a relationship with Arwen and b) decide to leave Middle Earth for the West now. So let's focus on that, rather than developing some crazy elaborate story that we can't really get on screen anyway.
So...what if this character is Arwen's friend in Lothlorien, a contemporary rather than a mentor? Sure, maybe she's a bit older than Arwen (born sometime in the 2nd Age), but she's not a 'mentor' - this Frame already has Galadriel (queen/grandmother) and Celebrían (mother), so another old/wise female elf would be rather redundant. She's Arwen's friend, and has been her companion whenever she visits Lothlorien. Arwen has two brothers, but no sisters, so perhaps she has a sisterly relationship with this character. I mean, friendship doesn't require a lot of explanation - we just show scenes of them together enjoying each other's company. Arwen can be sad in Episode 1, spend Episode 2 at the festival (where her friend appears), and then Episode 3 is them talking about her reasons for leaving and the farewell. That would give us all the reason for the 'immediacy' of this question that we would need, and some of the friend's arguments could mirror some of the arguments from the Debate. But we would eliminate the need for an elaborate back story for this character, and the distance of messengers from Rivendell telling Arwen what happened. We also would have the parallel with Míriel having to say goodbye to her family (sister) when she leaves with the Noldor. IF we want this character to tie-in directly to the Debate at Cuiviénen, it could come up that this elf is Avari, and her parents or grandparents were there. She could be the granddaughter of Nurwen, the same way as Arwen is the granddaughter of Celeborn. (or whatever) But perhaps part of the point of the story is that by leaving, this elf becomes a 'nobody' in Middle Earth. Arwen will go on to have a place in history....nameless friend from Lothlorien...will not. Arwen is young for an elf, but not actually young, so I think we can use this character to show that Arwen is not actually a teenager. They could have a long history together. Her friend could be married (perhaps she and her husband together are leaving?) They can bring up previous visits from a thousand years ago in a 'remember that time'? way.
I know this is not the character the hosts invented. My reason for doing it this way is that it was becoming very, very difficult to introduce an Avari mentor in Rivendell who is not there any more. So the real question is...does anyone else like the idea of giving Arwen a close friend in Lothlorien?
As for the Gollum subplot, the hosts liked the idea, but they did suggest doing it differently (and a lot less like the game). Their idea seemed to be that Arwen was riding out to deliver some humanitarian aid after hearing about their plight from some messenger. So, she's not personally staying out to catch the villain or anything - they can recount the story and we can show the viewers that it's Gollum, but Arwen isn't there to fight monsters.