The OP sounds very entitled: "We'd endorsed Slack to thousands of people on our Twitch.tv streams, and even mentioned it in interviews with the media."
Of course Slack must provide them with free chat rooms in perpetuity, they've even been mentioned in interviews!
It's probably better to be rid of "customers" like this sooner rather than later.
This whole concept of a 'customer' sounds very interesting, I hear they appreciate the services companies provide so much that they are willing to hand over actual money, instead of using the service they got for free to bitch about the service they got for free.
Agreed. This is more or less an example of patio11's "pathological customer": they won't or lack the resources to pay, have an unreasonable use case and overinflated expectations, and proceed to throw a fit loudly and publicly when they don't get their way.
If I were Slack I would generate migration assistants to get organizations like this OFF of Slack and on to something like Gitter ASAP. Seems like the return on that investment (in purely good will) would be much more predictable and scalable.