So far I interpret the results as brain circuits being strengthened by attentional focus training so that the prefrontal cortex can inhibit signals arising in the amygdala, insula, thalamus, and hypothalamus.

Might I suggest that as well as the inhibition you actually benefit from the cortex having more access to the information and processing that the aforementioned regions provide? Because generalised inhibition in itself isn't all that difficult, mindfulness aside. It is nuanced, well considered inhibition that takes work. It is also what lasts in the long term - because simply inhibiting the signals from those centres doesn't help eliminate the cause.