Best way to get synced audio from multi-cam Premiere project into Audition and back
Adobe Bridge should allow you to open the Sequence in Audition.  If you go to the project panel and right click the sequence you want to edit, you should be able to choose Edit and then Edit In Audition.  This will automatically bring the sequence over to Audition with the tracks properly laid out.  You should then be able to do any work you want to in Audition.

For output you have two options, you can either rely on Bridge to apply your changes from Audition when rendering the sequence or you can output a mix-down from Audition and then import it to Premiere and use it to replace the existing audio.  Since the project in Audition is synced to the Premiere sequence, the audio length should be correct starting from the beginning of the sequence.

More details are available in Adobe's online documentation here.