This thread's determination to have a cake and eat it too is outstanding. Our charge wants to live when Rits insists she must die, and you still avoid picking Rei's side. Why discuss Rei's humanity? Does it matter if she's technically human or not? Why consider disarming Rei, when the simplest way to put her at ease would be Misato picking up Ritsuko's gun and having Rits at gunpoint instead?
There's no achievable compromise in this situation, as Rei can't be partially alive. It's time to pick a side. This may be our last chance.
You are correct that we can't find a middle ground on that specific issue. However, the situation as a whole is more complicated.
Ritsuko wants to kill Rei. However, Rei also wants to kill Ritsuko. A significant component of why each wants to kill the other is fear that the other one is going to kill them. Preventing everyone from killing anyone is a compromise between these two positions. And if this makes both of them angry at Misato, that just means they're both alive.
EDIT: You know what, I have a better idea for how to get Rei's finger off the trigger.
[X] Grab Ritsuko's fallen gun and point it at your own head.
Very dramatic. I can imagine a version of this story where Ritsuko and Rei are shocked out of their current headspaces by this, giving Misato a chance to explain properly, and they both realize that Misato is doing this because she doesn't want
either of them to die.
I have nowhere near enough confidence that it would actually work out that way.
[X] If you two keep going, both of you are going to end up dead, and is Gendo, and Shinji, and Asuka, and everyone else in NERV. Do either of you think we can keep fighting back the Angels with either of you dead? Let alone both?
-[X] This is a standoff. The right move to play in a standoff is for both of you to lower your weapons, and
then discuss what to do next. We all - and that includes me - need to calm down a bit.
[X] Stand between Rei and Ritsuko.
-[X] Tell Rei and Ritsuko you won't allow them to kill each other despite everything.
-[X] Ask Rei if she wants to tell her friends that she killed somebody in cold blood. Ask her if she is really ready to kill Misato only to get Ritsuko? What about killing Shinji? Hikari? Asuka?
-[X] Tell Rtisuko to give you the PDA, shut up and stop escalating. Even she knows deep down that Rei is human, not some empty shell.
Both of these plans seem like they'd work.