> "That accumulating QBO statistics will either increasingly converge on Lunar statistics"

Validation of your premise:

The more data that is accumulated, the more the average converges to the theoretical prediction.

> "There is no doubt that QBO is slightly sensitive to Lunar tides, if not harmonically forced to high order."

Validation of your premise:

The first 3 lunar draconic (i.e. nodal) satellite harmonics (bottom red) clearly emerge from the entirety of the data -- at 0.423, 1.423, and 2.423 cycles/year. Harmonics such as this will not appear for any resonant phenomena, as those are required to be integral multiples of the fundamental frequency. This is clearly forced mixing (heterodyning) of a tidal signal with an annual impulse.