  The direct observability of coordinates x is often lost in PT-symmetric
quantum theories. A manifestly non-local Hilbert-space metric $\Theta$ enters
the double-integral normalization of wave functions $\psi(x)$ there. In the
context of scattering, the (necessary) return to the asymptotically fully local
metric has been shown feasible, for certain family of PT-symmetric toy
Hamiltonians H at least, in paper I (M. Znojil, Phys. Rev. D 78 (2008) 025026).
Now we show that in a confined-motion dynamical regime the same toy model
proves also suitable for an explicit control of the measure or width $\theta$
of its non-locality. For this purpose each H is assigned here, constructively,
the complete menu of its hermitizing metrics $\Theta=\Theta_\theta$
distinguished by their optional "fundamental lengths" $\theta\in (0,\infty)$.
The local metric of paper I recurs at $\theta=0$ while the most popular
CPT-symmetric hermitization proves long-ranged, with $\theta=\infty$.
