  We investigate the unitary dynamics following a sudden increase $\Delta U>0$
of repulsion in the paramagnetic sector of the half-filled Hubbard model on a
Bethe lattice, by means of a variational approach that combines a Gutzwiller
wavefunction with a partial Schrieffer-Wolff transformation, both defined
through time-dependent variational parameters. Besides recovering at $\Delta
U_c$ the known dynamical transition linked to the equilibrium Mott transition,
we find pronounced dynamical anomaly at larger $\Delta U_*>\Delta U_c$
manifested in a singular behaviour of the long-time average of double
occupancy. Although the real-time dynamics of the variational parameters at
$\Delta U_*$ strongly resembles the one at $\Delta U_c$, careful frequency
spectrum analysis suggests a dynamical crossover, instead of a dynamical
transition, separating regions of a different behaviour of the spin-exchange.
