As for a Hinata-Rin parallel connection .... it wouldn't make any logical sense. Sure, what little we saw of Rin depicted her as kind and sweet girl. She was mild-mannered like Hinata, not short-tempered like Sakura. That is a personality similarity, but it's not enough for a parallel by any means. In this case, Rin has to paralleled to another based on circumstance. Hinata never fell for the "cool kid", she fell for the "loser". Both suffered from unrequited love, but so did Obito. There's a clear issue here with an ObiRin/NaruHina parallel connection. Hinata almost died (Rin actually died), but it won't fit the situation. Do NH fans honestly believe Naruto will talk no jutsu Obito by mentioning Hinata almost dying for him? It's incomparable. There's a difference between a friend dying and a woman you loved dying. What's more is that Naruto's breakdown for HInata's near-death wasn't just because of her, it was just the trigger that unleashed all of his suppressed anger and stress (Village getting destroyed, Jiraiya dying, Kakashi dying). It was more of a "I can't take this anymore" moment of Naruto's, not a "The woman I love just got killed" moment. Comparing Obito's experience to Naruto's is like comparing apples to oranges.
Sakura, though different than Rin, fits the circumstance criteria needed for a Obito talk no jutsu. She held one-sided love for the skilled, cool guy in her team who loved no one romantically, while the loser teammate fell in love with her, but she simply cared for him. That's literally a mirror image of Part 1 Team 7.
Hinata will not be related to Rin or seriously injuried/killed to "change" Obito. The person who will go through that is Sakura and no one else.