We construct Alfvén wave-driven wind models for physical conditions appropriate to the expanding envelopes of cool, evolved stars. To derive wind properties, we assume steady, isothermal, spherically symmetric flow, but do not use the WKB (i.e., short-wavelength) approximation to calculate the wave amplitudes. Instead, we make use of the formalism developed in the first paper of this series (MacGregor & Charbonneau 1994), which describes wave reflection and associated modifications to the wave force, and consistently incorporates these effects into the treatment of wind dynamics.For flows containing undamped Alfvén waves of arbitrarily long wavelength we find that the occurrence of wave reflection has profound consequences for wind acceleration and mass loss. Specifically, in all of our computed models, the outward-directed wave force near the base of the flow is significantly reduced relative to that in comparable WKB models. As a result, the initial expansion speeds and mass flux densities of model winds that include non-WKB effects are smaller than those of corresponding WKB winds. Moreover, at large distances from the star, wave reflection leads to an enhancement of the wave force relative to models in which all waves are presumed to be outwardly propagating. This tendency, when combined with the previously noted reduction in mass flux, produces winds with higher asymptotic flow speeds than those driven by high-frequency, short-wavelength Alfvén waves. Given that the challenge of modeling winds from cool evolved stars is to produce winds with high mass fluxes and low asymptotic flow speeds, we argue that Alfvén waves provide an acceptable driving mechanism only if their wavelengths are sufficiently short that minimal reflection occurs near the base of the flow. For stellar parameters characteristic of a supergiant star with spectral type ∼K5, this translates into an upper bound on Alfvén wave periods of ∼1 day.