Here's another take I've been formulating for myself as to how I can get more out of Barry's idea of playing 6th on 5th. It seems like it's his way to label inversions of a chord, in a way that makes them more easily accessible (?) when soloing in the heat of the moment (Again, this is an evolving idea.)
Say I'm approaching a C7 chord. One way to think is a Mixolydian scale and its derivatives, my mind has always struggled with this academic method (I'm not knocking it and am getting better thinking this way.) So, with Barry's way, I see a Gmin6, I see that shape with a second on top, or I can see E-7b5 with the root being the 3rd of the dominant chord, or see the 3rd inversion, etc. I also can explore the academic idea, instead of Mixolydian, maybe I can think Locrian or min6 for scale ideas (I need to explore this more.)
As I said in my first post, I try to add this practice to routine, this way I'm hoping my brain will make connections.
I think it is best to work on all of Barry's ideas (1/2 rule, chromatic scale, 54321, etc.)