Today...I still didn't solve the problem, but I tried something different. Rather than a full class discussion (which sort of works but usually feels forced) or a backchannel discussion (which works until everyone starts typing and stops listening), or a lit circle discussion (which seems great in theory but usually people get distracted by the structure), and I simply had students pick small clusters of 3-5 and "talk about the play for 20 minutes". The key difference this time: not only did I circulate around the room, I had them all audio-record their work. While I haven't had a chance to listen to everything yet (and while I'm sure there's lots of vamping), I'm hoping this was a positive compromise between choice and structure. Students were given freedom to "discuss" without my intrusion, but they also knew there was some method of accountability.
As I type this, my final class is wrapping up their discussions for the day. I won't be able to hear the full results until tomorrow so I'll be forming no conclusions right now. While I don't expect this method to "fix" class discussions, hopefully it works as a better alternative than the discussion boards (which have been generally panned this year) and be used in varying contexts over the course of the year. They have the technology...might as well put it to use.