Janice doesn't know that. Beyond that, going "hey Control has gone crazy" is counterproductive since we're kind of relying on him to follow Control's orders to listen to the Traditionalist and not shoot her.
"FYI we're broken and off the rails" is also not something that Control would say or do, so your argument isn't even internally consistent.
I don't have enough brain to cover the "Janice doesn't know that" part. It would take a notable archive-dive to piece together exactly what she *does* know about Control, and I don't have that in me right now. The point isn't that Control would have sent her to say that it's broken and off the rails - it's that she'd imply that she was sent by one shard of Control - one that believes differently from the shard he's been listening to thus far, because there are a number of shards, and they're broken and off the rails.
...but, regardless,
I'm not saying this is a good plan. I didn't even say it was at the time. I can see the vague shape of a good plan that might conceivably be formed somewhere inside those sketched lines, but it would take a hell of a write-in (which I'm not capable of providing now, and don't really expect to be in the future) and still be pretty risky - just that the payoff might be worth it. If someone comes along with a way to turn my vague sketch into an actual fully-formed plan that is awesome, that's great, but I really don't expect it to happen. My point was more that, hey, the question in his mind is why Control set this up. That's the reason he's here. That's the burning question he wants answered. That's the thing that has his interest. In order to change his mind, we need to keep him interested, engaged, paying attention, thinking, learning. If we're not somehow leveraging the focus of his attentions when we know what they are, we're doing it wrong. It's by no means the only thing, but it's absolutely *a* thing. The vague and insufficient outline of a high-risk high-reward plan were just something I threw in there because it was the best I could come up with on the topic, and maybe they'd give someone else some inspiration.
Other vague thoughts... and it's 6-somethign AM here, so they're only somewhat coherent at some point, there's a good chance he's going to wonder why *we* decided to come here, and put ourselves in his power. One of the interesting tactical questions is whether or not we ever tell him (or, alternately, subtly let him know) how thoroughly we've put ourselves in his power, and how we use that. He... might recognize the earrings, for example, if they're from his own company. The fact that we're consciously and deliberately wearing his sign means something, and as a Syndic, he knows it means something. It might be a useful part in an Ethos challenge - part of the counterargument to the "she doesn't have the courage to have confidence in her convictions". Actually, I think the Ethos argument is going to be significantly strengthened is we can somehow sell the idea that moderation is actually one of our convictions. Right now, it looks like he's just using "has confidence in convictions" it as a codephrase for "is a radical". Of course, that's going a bit metagame - the info was gained while she was offscreen - and we don't want to dip too heavily from that well. Might not be worth it after all. Mostly, I'm just trying to dig up chunks of ore for other folks to use.