  The twist-and-turn dynamics of spin squeezing result from the interplay of
the one-axis-twisting- (nonlinear in the collective-spin operators) and the
transverse-field turning (linear) term in the underlying
Lipkin-Meshkov-Glick-type Hamiltonian, both with constant (time-independent)
coupling strenghts. Using the methods of shortcuts to adiabaticity (STA) and
their recently developed enhanced version (eSTA), we demonstrate here that
dynamics of this type can be utilized for a fast and robust preparation of
spin-squeezed states in internal bosonic Josephson junctions -- condensates of
cold bosonic atoms in two different internal (hyperfine) states (single-boson
modes) coupled through Rabi rotations. Assuming that the initial state of this
system is its ground state for a given initial value of the (time-dependent)
linear-coupling strength and that the nonlinear-coupling strength remains
constant, we set out to determine the time-dependence of the linear (Rabi)
coupling strength that allows for the generation of spin-squeezed states using
the STA- and eSTA-based approaches. We then characterize the modified
twist-and-turn dynamics of this system by evaluating the
coherent-spin-squeezing- and number-squeezing parameters, as well as the
fidelity of the target spin-squeezed states. In this way, we show that the eSTA
approach allows for a particularly robust experimental realization of strongly
spin-squeezed states in this system, consistently outperforming its adiabatic
and STA-based counterparts, even for systems with several hundred particles.
