  The interplay of charge, spin, lattice, and orbital degrees of freedom leads
to a wide range of emergent phenomena in strongly correlated systems. In
heterobilayer transition metal dichalcogenide moir\'e systems, recent
observations of Mott insulators and generalized Wigner crystals are well
described by triangular lattice single-orbital Hubbard models based on K-valley
derived moir\'e bands. Richer phase diagrams, mapped onto multi-orbital Hubbard
models, are possible with hexagonal lattices in $\Gamma$-valley derived moir\'e
bands and additional layer degrees of freedom. Here we report the tunable
interaction between strongly correlated hole states hosted by $\Gamma$- and
K-derived moir\'e bands in a monolayer MoSe$_2$ / natural WSe$_2$ bilayer
device. To precisely probe the nature of the correlated states, we optically
characterise the behaviour of exciton-polarons and distinguish the layer and
valley degrees of freedom. We find that the honeycomb $\Gamma$-band gives rise
to a charge-transfer insulator described by a two-orbital Hubbard model with
inequivalent $\Gamma_\mathrm{A}$ and $\Gamma_\mathrm{B}$ orbitals. With an
out-of-plane electric field, we re-order the $\Gamma_\mathrm{B}$- and K-derived
bands energetically, driving an abrupt redistribution of carriers to the
layer-polarized K orbital where new correlated states are observed. Finally, by
fine-tuning the band-alignment, we obtain degeneracy of the $\Gamma_\mathrm{B}$
and K orbitals at the Fermi level. In this critical condition, stable Wigner
crystals with carriers distributed across the two orbitals are observed until
the Fermi-level reaches one hole per lattice site, whereupon the system
collapses into a filled $\Gamma_\mathrm{B}$ orbital. Our results establish a
platform to investigate the interplay of charge, spin, lattice, and layer
geometry in multi-orbital Hubbard model Hamiltonians.
