We demonstrate the feasibility of probing the charged lepton-flavor-violating decay μ^{+}→e^{+}X^{0} for the presence of a slow-moving neutral boson X^{0} capable of undergoing gravitational binding to large structures and, as such, able to participate in some cosmological scenarios. A short exposure to surface antimuons from beam line M20 at TRIUMF generates a branching ratio limit of ≲10^{-5}. This is comparable to or better than previous searches for this channel, although in a thus-far-unexplored region of X^{0} phase space very close to the kinematic limit of the decay, where m_{X^{0}} approaches m_{μ^{+}}. The future improved sensitivity of the method using a customized p-type point-contact germanium detector is described.