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Efforts to push the spatiotemporal imaging-resolution limits of femtosecond laser-driven ultrafast electron microscopes (UEMs) to the combined angstrom–fs range will benefit from stable sources capable of generating high bunch charges. Recent demonstrations of unconventional off-axis photoemitting geometries are promising, but connections to the observed onset of structural dynamics are yet to be established. Here we use the in-situ photoexcitation of coherent phonons to quantify the relative time-of-flight (r-TOF) of photoelectron packets generated from the Ni Wehnelt aperture and from a Ta cathode set-back from the aperture plane. We further support the UEM experiments with particle-tracing simulations of the precise electron-gun architecture and photoemitting geometries. In this way, we measure discernible shifts in electron-packet TOF of tens of picoseconds for the two photoemitting surfaces. These shifts arise from the impact that the Wehnelt-aperture off-axis orientation has on the electron-momentum distribution, which modifies both the collection efficiency and the temporal-packet distribution relative to on-axis emission. Future needs are identified; we expect this and other developments in UEM electron-gun configuration to expand the range of material phenomena that can be directly imaged on scales commensurate with fundamental structural dynamics.