Aircaps demos show it to be pretty fast and almost real time. Meta's live captioning works really fast and is supposed to be able to pick out who is talking in a noisy environment by having you look at the person.
I think most of your issues are just a matter of the models improving themselves and running faster. I've found translations tend to not be out of whack, but this is something that can't really be solved except by having better translation models. In the case of Airpods live translate the app will show both people's text.