  Hard, non-thermal, persistent pulsed X-ray emission extending between 10 keV
and $\sim 150$ keV has been observed in nearly ten magnetars. For
inner-magnetospheric models of such emission, resonant inverse Compton
scattering of soft thermal photons by ultra-relativistic charges is the most
efficient production mechanism. We present angle-dependent upscattering spectra
and pulsed intensity maps for uncooled, relativistic electrons injected in
inner regions of magnetar magnetospheres, calculated using collisional
integrals over field loops. Our computations employ a new formulation of the
QED Compton scattering cross section in strong magnetic fields that is
physically correct for treating important spin-dependent effects in the
cyclotron resonance, thereby producing correct photon spectra. The spectral
cut-off energies are sensitive to the choices of observer viewing geometry,
electron Lorentz factor, and scattering kinematics. We find that electrons with
energies $\lesssim 15$ MeV will emit most of their radiation below 250 keV,
consistent with inferred turnovers for magnetar hard X-ray tails. More
energetic electrons still emit mostly below 1 MeV, except for viewing
perspectives sampling field line tangents. Pulse profiles may be singly- or
doubly-peaked dependent upon viewing geometry, emission locale, and observed
energy band. Magnetic pair production and photon splitting will attenuate
spectra to hard X-ray energies, suppressing signals in the Fermi-LAT band. The
resonant Compton spectra are strongly polarized, suggesting that hard X-ray
polarimetry instruments such as X-Calibur, or a future Compton telescope, can
prove central to constraining model geometry and physics.
