Mentioned in the OP, but perhaps buried a bit, I am always partial to Chebyshev's Inequality (https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.

Mentioned in the OP, but perhaps buried a bit, I am always partial to Chebyshev's Inequality (https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/Chebyshev%27s_inequality) since it describes all distributions not just Gaussian. While approximations, they are nice to have when you question the normality of the data and still want to estimate limits - more numbers to remember however, since they are estimates.