We use wirecast to encode our streams, you can monitor the sound on it and it also has an audio delay feature – up to 1s. Touch wood we have never had any issues with it and the ATEM TVS. We are using Blackmagic Intensity Extreme’s to get the video in but have used intensity pro on Windows machines too with no problems.
We used Flash Media Encoder for a while but found it frustrating and wirecast has been well worth the outlay.
We pump the sound in via the jacks on our HDMI-SDI converters but using the mic inputs on your cameras would do the same job. We have also used the inputs on the breakout cable with the extremes but doing it this way means you cannot record sound directly from the TVS via the USB connection.