Got it - I had no idea there was an existing integration. 
Thanks!
The primary issue here is that Parent Window queries don't behave like normal queries, both in the way they are triggered and in the way they handle callbacks. This isn't well documented, at best, and actually feels a bit buggy. I'll talk to the team and take a closer look!
Fortunately, there's an effective - though admittedly quirky - workaround:
This works because getConvo.data automatically updates when selecting a new conversation in Missive, which in turn causes triggerOnConvoChange to run. This particular query doesn't actually do anything except listen for changes and, upon completion, update the value of convoData.
I hope this helps! Let me know if you have any questions and I'll follow up here with any of my own updates.