I wrote a tutorial in December on my method for working with 5.1 audio:

https://www.vegascreativesoftware.info/us/forum/5-1-surround-render-only-see-stereo-options--125867/

Mr. fr0sty is correct with what he wrote. To expand on that, it depends on how the app you use to listen to multichannel audio maps those channels into your 2-channels headphone environment that determines which ear hears which channel. If your listening app maps the center channel (channel 3 -- the way I work with multi-channel audio) all the way to the left, that's only where you hear the center channel.

Sorry T. But to me that doesn't exactly sound like a proper solution due to the complex layered nature of the audio in this production.

Your solution is to not use 5.1 audio at all if you are not mixing it on an actual 5.1 channel surround system connected to an audio interface that can output 6 discrete channels to the audio amplifier, which can also receive them (either over 6 individual analog inputs per speaker, or HDMI. Optical will not work). That is the only way to edit 5.1 channel audio.

The only difference in complexity for any project that I can see depends on how many raw tracks you're working with. Regardless, the process is the same.

By nature, 5.1 surround is a complex beast. In any case, it comes down to sub-mixing each track at the proper level, then assigning those tracks to the proper channel of six, then outputting a file that handles at least six discrete channels. My .mxf method outputs up to eight audio channels.

If you do not have a proper 5:1 monitoring system.. mix in stereo. An improper multichannel mix can result in total loss of important channels when down-mixed. A basic stereo mix is more fool-proof all around.