  We consider isotropic and monochromatic photon emissions from equatorial
emitters moving along future-directed timelike geodesics in the near-horizon
extremal Kerr (NHEK) and near-horizon near-extremal Kerr (near-NHEK) regions,
to asymptotic infinity. We obtain numerical results for the photon escaping
probability (PEP) and derive analytical expressions for the maximum observable
blueshift (MOB) of the escaping photons, both depending on the emission radius
and the emitter's proper motion. In particular, we find that for all
anti-plunging or deflecting emitters that can eventually reach to asymptotic
infinity, the PEP is greater than $50\%$ while for all plunging emitters the
PEP is less than $55\%$, and for the bounded emitters in the (near-)NHEK
region, the PEP is always less than $59\%$. In addition, for the emitters on
unstable circular orbits in the near-NHEK region, the PEP decreases from $55\%$
to $50\%$ as the orbital radius decreases from the one of the innermost stable
circular orbit to the one of the horizon. Furthermore, we show how the
orientation of the emitter's motion along the radial or azimuthal direction
affects the PEP and the MOB of the emitted photons.
