Dear Mr. Jamali:
Your essay includes some very deep insights into the nature of quantum mechanics. You are asking the right questions.
For example, you ask about the quantum frequency, and suggest a relativistic theory associated with a rotating field. You further suggest a classical background theory with a filtering processing for quantization, and point out that a complex wave cannot be a real physical field.
You might be interested in my alternative quantum theory, which would seem to fit your criteria. This was addressed in my previous FQXi essay, "Fundamental Waves and the Reunification of Physics", and again in my new FQXi essay, "The Uncertain Future of Physics and Computing".
I have referred to this as a neoclassical synthesis, with a real quantum wave which is a rotating vector field, such as one would have with a circularly polarized EM wave. This follows the vector Klein-Gordon equation, with the additional ansatz that the only acceptable solutions correspond to rotation about a fixed axis with a quantized spin. Suppressing the "carrier wave" rotating at mc^2/h, leads directly to the complex Schrodinger equation, where the complex phase is a relative phase angle of the real vector field. This is not statistical, and there are no point particles.
I argue that quantization cannot be achieved in a linear equation, but rather requires a soliton-like solution of a nonlinear equation, which reduces to the linear KG equation for spin-quantized solutions. The complete nonlinear equation has not yet been identified.
This picture has no microscopic indeterminacy, no superposition, no entanglement, and indeed, no Hilbert space. It also makes accessible experimental predictions that contrast sharply with orthodox QM. It also says that quantum computing is impossible. This is currently a hot field of technology - my prediction is that it will fail completely.
Alan Kadin