I'm intrigued by this but not sure the platforms we use make it straightforward to do so. I spent some time looking at Android documentation and there appears to be no way to control the audio channels that speech output goes to. On iOS you can do it, but as an all-or-nothing thing, i.e. we could have both channels or left only for example.
Beyond that and we're looking at a much more expensive feature, to synthesize the audio to disk or memory and adjust the balance ourselves.