Let's say I have 2 audio tracks (A + B) and (A + C), I know that I can invert one of these tracks and get the difference between these 2 tracks (B + C). Is there anyway of comparing them to return the audio that is the same between the 2 tracks (A)?
Basically you are wanting to un-mix an omelette. There's not too many ways to do this successfully, but it is a common question on this stack.
There is not a quick and easy solution, although you are not the first person to go looking for one.
If I was you, I would be looking for solutions in the DSP stack, but also investigate correlation, cross-correlation and auto-correlation. I am not aware of any plugins for DAW's that do this, but there may be some software around that can have a crack at it. I am thinking specifically of matlab.