"In what fields have Buddhist monks excelled?"
Martial arts? Some other arts. Propagating a religion. Overcoming what seem to many people to be overwhelming motivations, such as the motivation to eat or to avoid extreme amounts of pain, convincing people that they are wise, maybe some memory and rapid cognition feats.

If you count Stoics as Buddhists, as I would, governing Rome & providing that part of the content of Christianity for lack of which the ancient world seems most alien.

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.

Do you have statistics or studies concerning the claim that Buddhist physicists are not advantaged in science? How would you even begin to rationally approach the issue? It seems complicated---you'd have to adjust for education levels, the possibility that meditators are inclined to pursue subjects other than physics, the fact that meditation takes up time that could otherwise be devoted to studying physics, different cultural backgrounds of meditations vs. controls...

Intuitively, I think your claim is likely to be true, but I can't really see how you can rigorously support it. Data on the % of Buddhist physicists, if it even exists, would only be scratching the surface of what you would need to support your claim. (Not that I want to debate the claim. But if you feel it's important, I want a non-handwavey argument.)

A better model for enlightenment, meditation and rationality, I'd say, is that these things give you tools that allow you to be more rational if you're so inclined. As with everything in life, it's your own goals and inclinations that determine what you do with them.

An analogy is drinking coffee. Paraphrasing Paul Erdos, a mathematician is one who turns coffee into theorems. Do coffee drinkers have a special advantage in mathematics? Probably not. So perhaps Erdos was wrong; perhaps having to empty one's bladder more often actually interferes with being a good mathematician? Again, probably not. Most likely, drinking coffee leads to mathematical productivity for people who are interested in increasing mathematical productivity.

*Buddhist