Welcome Marisa
I have felt the same feeling as a benzo from a herbal medication with valarian extracts in it. I hardly ever use benzo's anyway but it really goes to show how powerful the mind is.
I kind of like your idea of associating a particular mantra with being relaxed. The mind is all about association. A bayesian probalistic network of learning...
What you are saying is exactly why the FDA are suggesting that certain drug trails include people who are unaware of being given a drug. How they will get the ethics right is complicated but they have recognised the powerful effect of the placebo and the flaws in trails were there are only placebo and drug groups.