Thanks, fascinating insights. I think an everything-to-everything multimodal model could work if it's big enough because of transfer learning (but then there are latency issues), and so could a refined system built on LLMs/LMMs with TTS (like what you are using), but I haven't seen any good research on audio-to-audio language models. My suspicion is that that would take a lot of compute, much more than text, and that the amount of semantically meaningful accessible data might be much lower as well. And if you do manage to get to the same level of quality as text, what is latency like then? Not 100% sure, just intuitions, but I doubt it's great.
I like the idea of an RL predictor for interruption timing, although I think it might struggle with factual-correction interruptions. It could be a good way to make a very fast system, and if latency on the rest of the system is low enough you could probably start slipping in your "Of course", "Yeah, I agree", and "It was in March, but yeah" for truly natural speech. If latency is low you could just use the RL system to find opportunities to interrupt, give them to the LLM/LMM, and it decides how to interrupt, all the way from "mhm", to "Yep, sounds good to me", to "Not quite, it was the 3rd entry, but yeah otherwise it makes sense", to "Actually can I quickly jump on that? I just wanted to quickly [make a point]/[ask a question] about [some thing that requires exploration before the conversation continues]".
Tuning a system like this would be the most annoying activity in human history, but something like this has to be achieved for truly natural conversation so we gotta do it lol.