  We present a quantitative, near-term experimental blueprint for the quantum
simulation of topological insulators using lattice-trapped ultracold polar
molecules. In particular, we focus on the so-called Hopf insulator, which
represents a three-dimensional topological state of matter existing outside the
conventional tenfold way and crystalline-symmetry-based classifications of
topological insulators. Its topology is protected by a \emph{linking number}
invariant, which necessitates long-range spin-orbit coupled hoppings for its
realization. While these ingredients have so far precluded its realization in
solid state systems and other quantum simulation architectures, in a companion
manuscript [1901.08597] we predict that Hopf insulators can in fact arise
naturally in dipolar interacting systems. Here, we investigate a specific such
architecture in lattices of polar molecules, where the effective `spin' is
formed from sublattice degrees of freedom. We introduce two techniques that
allow one to optimize dipolar Hopf insulators with large band gaps, and which
should also be readily applicable to the simulation of other exotic
bandstructures. First, we describe the use of Floquet engineering to control
the range and functional form of dipolar hoppings and second, we demonstrate
that molecular AC polarizabilities (under circularly polarized light) can be
used to precisely tune the resonance condition between different rotational
states. To verify that this latter technique is amenable to current generation
experiments, we calculate from first principles the AC polarizability for
$\sigma^+$ light for ${}^{40}$K$^{87}$Rb. Finally, we show that experiments are
capable of detecting the unconventional topology of the Hopf insulator by
varying the termination of the lattice at its edges, which gives rise to three
distinct classes of edge mode spectra.
