There is an add-on for exporting the audio to Ardour: http://blendervelvets.org/en/blue-velvet/
And if you export the video as one file, it can be added to Ardour too, so you'll be editing the audio in a DAW while watching the video in sync. However, Ardour is only free, if you know how to build it yourself, or you'll have to pay "something".
Alternatively, there is an EDL export add-on(text-file), which will allow you to export info for one video track and four audio tracks, but ex. Davinci Resolve will not import audio from EDL files - in D.R. EDL files are only used for conforming video edits. https://github.com/tin2tin/ExportEDL
Third option add-on-wise is to use this add-on to roundtrip single audio clips in ex. Audacity: https://github.com/Joeboy/blender-addons/blob/master/open_strip_source.py This one does not work right away on Win 8, because you'll have to manually add the full path for audacity.exe. I might add some more functionality to this add-on, to make it more user-friendly.
Jack could be used on Linux to control an external volume monitor: https://audaspace.wordpress.com/2010/02/21/jack-transport/
Last option is to export each channel as a stem audio file(just one file pr. track with beep for sync) and import those in a DAW and make cuts where needed.