The equation Q=Cv sqrt(dp/G) is, in fact derived from the bernoulli eqn. My old freshman physics book shows the derivation of dp=1/2 rho (v2^2-v1^2) and goes on to modify it for negligible v1. Regarding it's accuracy, remember this is for incompressible, inviscid flow. The term Cv is an empirical factor for the huge energy loss you referred to.
I believe the ANSI/ISA 75 papers you ordered are about the best resources I've seen to account for viscosity, choking and compressibiliy. They are very practical, but don't give a lot of theoretical justification to the equations. Also, they relate well to the Fischer Gate Valve litersture.

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