You want what is common to both L and R and reject everything else ? : that’s “centre pan isolation”, a.k.a. “centre pan extraction”.
The result of the inversion trick is what is not common to both channels: i.e. “centre pan removal”, (the opposite of what you want).
There is a free plugin which works with Audacity 1.3.11 which will do centre pan isolation it’s called Kn0ck0ut.
Similar plugins and standalone software which does this are available, (NB the results are not perfect: usually lots of digital artifacts).
Of course when centre pan isolation is applied to a stereo track the result is mono.