ProTools (and LogicProX, apparently) has 'strip silence' which can lift out the sections that are below the threshold - so you could step through and tighten up the conversation. Theres a feature request you can vote on. I don't think, from my very limited understanding of it, that the Audition 'remove silence' option will do you many favours. It's destructive & you can't set different thresholds for individual tracks. Presumably you'd have to deal with the tracks in an interleaved format, or as a mixdown, as if you deal with them as individual tracks then you will lose the relationship between them. You are stuck with doing it manually, although the pull up should be fairly consistent so you may be able to speed it up with a macro.
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