Sayaka doesn't let go of her dislike of people and in this case it might cross over into actual hate.
Sayaka is selfish at heart, that's why she tends to self-destruct in such a way with no regard to those around her.
If she can't live on her terms, she'll die on them instead.
This is exactly what we must break the blueberry of. Note that we're not going to be able to do that if Sayaka labels us a liar and a manipulator.
On the plus side, we've already making progress, in that we've gotten her to change her mind about Homura. Even Homura recognizes the rarity and difficulty of this feat: it's in fact why she's actually allowing herself to feel hope and be a little vulnerable again. This, in my opinion, is a victory that we can build upon, to reforge Sayaka into a less rigid, and therefore less brittle, personality.
On the minus side, she still has that stubborn sense of personal honor. She calls it heroism, but really it's selfishness, the belief that she must succeed on her own merits or not at all. It's a dangerous belief for so green a meguca to have, and we must break her of it before she rejects any and all help, resulting in Octavia.
In this way, Oriko is, IMO, the perfect teachable moment, because she also has the same selfishness, a selfishness that led her to rely wholly on her power rather than thinking things through first, and resulted in her breaking Hitomi's leg and burning down Sayaka's house in the name of her Greater Good. That's the problem with only gathering sycophants around you, as Oriko did, or worse still never listening to anyone else and relying only on yourself, as Sayaka does: there's no one to call you out when you're doing something bone-headed, like
making a selfish wish and selling your soul to an alien used car salesman. We really need to pound this lesson hard into Sayaka, for reasons that go far beyond getting her to become friends with O+K, though it does seem to me a likely side-effect of teaching her this lesson is at least a detente between Sayaka and O+K.
(This conversation, BTW, should be had in front of Madoka, but probably not anywhere near Oriko+Kirika: Sayaka won't likely be ready to meet those two for days, maybe weeks. OTOH, this is also a good way to further hammer in the essential selfishness of what Sayaka just did, in order to further persuade Madoka to not do the same thing.)