We present a detailed modeling and computation methodology to determine the optical Cherenkovsignals produced by upward-moving extensive air showers (EASs) induced byτ-leptons and muons,sourced from the interaction of high-energy astrophysical neutrinos interacting in the Earth. Fol-lowing and extending the physics modeling and Cherenkov signal simulations performed in [1], thisscheme encompasses a new, state-of-the-art computation of the muon neutrino propagation insidethe Earth and the contribution to theτ-lepton muon decay channel. The modeling takes into ac-count all possibleτ-lepton decay and muon energy loss channels that feed the optical Cherenkovemission, produced by both tau and muon initiated EASs. The EAS modeling uses the electronenergy, angular, and lateral distributions in the EAS and their evolution as well as the wavelengthdependence of the Cherenkov emission and its atmospheric attenuation. The results presented hereare focused on the detection capabilities of sub-orbital (balloon-borne) and orbital (satellite) basedinstruments. The latter case was calculated for POEMMAato compare to that presented in [1],specifically including the muon-decay channel ofτ-leptons and the muonic EAS Cherenkov signalfrom muon neutrino interactions in the Earth. By detailing all these individual contributions tothe optical Cherenkov emission and detection, we show how the ensemble that includes muonicchannels provides a large detection capability for space-based, high-energy cosmic neutrino detec-tion. Specifically, we show that for neutrino energies∼<10 PeV, the upward-EAS sensitivity due tomuon neutrino interactions in the Earth begin to dominate over that for tau neutrino interactions,effectively extending the neutrino sensitivity to lower energies.