Hi Jon,
When moving an A6 chord two frets down, you do get a G6 chord. However, you also get an (implied) A9 chord.
Let’s look at the chord tones:
A6 = (A, C#, E, F#)
Moving that down two frets gives (G, B, D, E) = G6.
Now, the chord tones of A9 are (A, C#, E, G, B). Drop the A and C#, and you get the chord tones of G6. So, that G6 chord can be viewed as an A9 chord without root (presumably played by the bass) and without 3rd (presumably played by the rhythm section).

This sort of juggling is frequent with rich chord.
Hope this helps.

That’s fine, but there would have to be something else in the context to make it imply an A9.

There’s no root and you are missing the third, which are the two elements that most clearly define a chord. The third strongest element is the seventh, in this case the G. But this 7th is in the bass, which is probably the hardest place for our ears to get used to it.

So it may be an A9, but it’s probably more implied by what comes before and after it.

Well…

Jean-Michel G wrote:

… So, that G6 chord can be viewed as an A9 chord without root (presumably played by the bass) and without 3rd (presumably played by the rhythm section).

As for the voicing, if the bass plays the root and if the rhythm section plays the 3rd, then the 7th isn’t in the bass anymore 😉