We demonstrate the feasibility of probing the charged lepton-flavor-violating decay μ⁺ → e⁺X⁰ for the presence of a slow-moving neutral boson X⁰ 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 X⁰ phase space very close to the kinematic limit of the decay, where mX0 approaches m_μ⁺. The future improved sensitivity of the method using a customized p-type point-contact germanium detector is described.