In a journey of infinite undiscovery and breaking things on my phone, I've found that the native Talk/Gchat application on Android doesn't support multiple accounts signed in (and in fact, doesn't support even changing the one account without serious issues).

I found another application, and I'm running. If you feel like you want to IM me (for free, rather than paying for a text), talking to me at j.to.the.rho AT gmail.com. I'll have to confirm your request first.