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The paper [R .T. Sandberg and A. G. R. Thomas, Phys. Rev. Lett. 130, 085001 (2023)] proposed a scheme to generate ultrashort, high energy pulses of XUV photons through dephasingless photon acceleration in a beam-driven plasma wakefield. An ultrashort laser pulse is placed in the plasma wake behind a relativistic electron bunch so that it experiences a density gradient and therefore shifts up in frequency. Using a tapered density profile provides phase-matching between the driver and witness pulses. In this paper, we study via particle-in-cell simulation the limits, practical realization, and 3D considerations for beam-driven photon acceleration using the tapered plasma density profile. We study increased efficiency by the use of a chirped drive pulse, establishing the necessity of the density profile shape we derived as opposed to a simple linear ramp, but also demonstrating that a piecewise representation of the profile—as could be experimentally achieved by a series of gas cells—is adequate for achieving phase matching. Scalings to even higher frequency shifts are given.