A mirrorless or even an older DLSR will be a marked improvement for meeting with colleagues as well. They use HDMI out, and they aren't really be suggested for audio, so neither of the factors you mentioned are even involved.

Of course if you sound like crap and can't stream at a decent bitrate, fix that first / as well. But with crisp audio and a decent Net connection, there's plenty of room to improve video quality from awful to decent, and your colleagues notice both, whether they realize it or not.