I don't think this is accurate. The key mediating variable for reduced anxiety is having a mystical experience, and one of the defining characteristics of the mystical experience is that it feels more real than real life. C.f. csp.org/psilocybin
"Physicalism, by contrast, could be easily falsified. If science ever established the existence of ghosts, or reincarnation, or any other phenomenon which would place the human mind (in whole or in part) outside the brain, physicalism would be dead."
I know he's just quoting Harris here, but this is BS. There is literally no known phenomena which you couldn't explain away with some as yet undiscovered materialist phenomena. C.f consciousness, spooky action at a distance, etc.
"Many years later, I have yet to have a mystical or religious or peak experience which could either convert me or leave me unmoved, and thus empirically settle the issue as to why I am an atheist - absence of experience, or reasoned belief?"
Given that 80% of people have these experiences in the lab while on psilocybin, if you are judging without having had these experiences yourself then that's just lazy. Even if you don't want to go the drug route, the vast majority of people also have chakra type experiences within the first few days of taking up meditation in a retreat setting.