[x] Yumi's concerns are mostly practical, right? What can you do to address them?
-[x] She's a practical person, so let's try for reasoned debate. We do understand her position, but we also believe that her claim that we're going to crash, burn, and get ourselves and everyone around us killed is incorrect, and we'd like a chance to convince her of that if she doesn't mind spending the time to talk it over with us. A bit of conversation is a reasonable enough request, right?
I think the above is the right sort of opener, regardless of what actual points we make following. Yumi might not actually be logical, but she tries to present herself that way even to herself. She wants to believe that she's doing the most intellectually optimal thing, and further, wants other people to agree with her. Yui is enough of a social chameleon that I'm willing to bet that we can successfully engage her on that playing field, given the right points; it's come up before that Yui tries to adapt her conversational strategies to whatever will appeal most to whoever she's talking to, so a one-on-one debate about philosophy and morality actually plays surprisingly well to her strengths.
We just need Yumi to agree that sitting down for an hour over ice cream or something and talking about how idealism is the optimal game theory strategy in our situation, sticking corpsicles into freezers until we have therapy and mind control to bring to bear is not a high-cost decision and has side benefits she's not appreciating, and surrounding ourselves with enough experienced advisors to mitigate the worst excesses of our personal beliefs is actually a more successful strategy than slinking off on her own to lay low/find an isolated territory/join a likely group elsewhere. If we can logic her into agreeing that her expected lifespan is longer with us than elsewhere, we'll have her.
Additional subpoints will be needed, obviously; this is just trying to reset the stage for our argument from "sweeten your offer or I'm ditching" to "I don't think you appreciate the worth of what's on the table and here's why".