Switch from a headset mic to a handheld mic and teach the mouth-breather to speak off axis so the heavy breathing won't be as noticeable. That will also keep some of the moisture off the mic. Could you be hearing plosive sounds rather than breathing? This can be fixed with a pop filter and you can attach it to the mic stand. As for your whisperer, well, maybe after practicing a few times the child will feel more confident and will speak up.