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And so I'm left with the idea of just having a freenode channel, with @whitequark's logging bot in it, letting people bridge in via the Matrix bridge at least until that becomes a problem, and calling it a day...
Yes, it's terrible, it's plain text only, it has no sane file transfer, it has no log integration, it's not particularly newbie-friendly... but nothing else seems to be strictly better in enough ways.
And at least I already know how it works and so do most FOSS devs. 
I haven't made my decision yet, feel free to try to change my mind.
To everyone saying Discord this Discord that: look, I'm in more Discord servers than IRC channels these days, I get Discord. I still think it's not the right option for this project, and enough people I care about would never use it.
One thing that *might* end up happening is dev chat on IRC, user chat on Discord, or something along those lines.
Have you tried gitter? I've worked on a project that uses it. I use it via their IRC bridge, which works pretty well. Never tried their web client or their phone apps.
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Requirements: open protocol, data portability, cloud hosted (but option to self-host).