My crew can normally get around this because we're all in TS together, but it's still quite frustrating when you have a full lobby trying to figure out who's bringing what, and you can't hear your own teammates. I have even gone in and muted GoI while I figure out what's going on in TeamSpeak. It would be nice to toggle even just the opponent's voice chat, or just my own ship's voice chat. The only problem is this might be abused.
In the end, I normally just use the text crew-chat and for the especially stubborn gunner who I'm trying to tell to go engi, a PM normally works pretty well since it pops up on their screen.