Ah, ok you are essentially going the the opposite way, making a Sum/Difference stereo-width manipulation of an existing Left/Right stereo signal.
Just mix it down, the output from the master bus that you are hearing is the L/R stereo output that has been "enhanced" by way of the Sum/Difference processing you've set up.
The easy way to do the same is to use a stereo width plugin. Such a plugin can make the stereo width narrower, which is equivalent to simply panning both Left and Right channels closer to center. Not much special about that, but it can also make the stereo width "wider than normal" which in essence "pans farther than hard Left/Right" by introducing some Left channel with inverted polarity to the Right output and some Right channel with inverted polarity to the Left output. To do that simply without using a plugin or a built in stereo widener control (not sure about Audacity, but a number of DAWs have such a function built in, often as part of the stereo balance control on any stereo input channel, or maybe just the master bus), you can copy the left channel to a open mixer channel, invert polarity, and pan it fully right. Do the opposite with the right channel. Then bring each of those two new channels up a little bit in level and the stereo output of that mixed with the original channels will go "overwide" or what is sometimes referred to as "super-stereo". You only be able to add so much before it gets "overly phasy sounding" and starts getting less wide again in a weird way. If your goal is just a bit of widening, you don't need to also make an additional mono Sum channel (Mid). Just mix those two inverted polarity / opposite panned channels with the original L/R channels. Essentially, this method just increases the amount of Side (Difference) signal in the mix.
If your goal is more extensive Sum/Difference processing, then it makes sense to convert Left/Right to Sum/Difference, do what ever you wish to do in that mode (change stereo width, or otherwise process the center imaging content differently than the content that images out toward the left and right sides - it's a very powerful way of manipulating stereo) and then convert back to Left/Right again. Seems to me the process you describe is more akin to this.
^ Many stereo plugins (stereo width adjusters, EQ's. compressors, reverbs, whatever) can be switched run in Sum/Difference mode rather than Left/Right mode. Some of them will refer to that as Mid/Side mode rather than Sum/Difference mode, which does somewhat better describe which part of the resulting stereo stereo image it is targeting. Using such a mode in a plugin makes all this very easy since both the L/R to Sum/Difference conversation that precedes the primary plugin effect and the Sum/Difference conversion back to L/R again afterward is done automatically inside the plugin.