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.