I'm my opinion, the best bet that your suggestion may be true is *Classical Stochastic Electrodynamics*.  This theory is not very well known, and still in its development phase.  But its ideas are very interesting.  See there :

https://en.wikipedia.org/wiki/Stochastic_electrodynamics

https://arxiv.org/abs/1205.0916

In brief :  Stochastic Electrodynamics (SED) postulates that the vacuum is filled with zero-point fluctuations of the electromagnetic field, that can be described classicaly.  It's just a stochastic field that is there, isotropic, homogeneous, and have a Lorentz invariant spectrum.  Yet, this random field have an effect on the motion of particles, and the observer can only see some average behaviors.  This theory *suggest* that QM is a kind of *effective theory*, valid for some time and space averages only.  It can also reproduce most of the formalism of QM, but it's mathematically a very complicated theory.

The Planck constant enters that theory as a *classical constant* that defines the *scale* of the random field.  All (most ?) of QM follows from that.