Nuclear physics aims to treat both bound and unbound states using a general predictive method. The position-space quantum Monte Carlo (QMC) methods have accurately computed bound-states for A<13 but have yet to see significant adaptation to unbound systems. In this work, we apply a successful numerical method to extend the types of possible unbound-state calculations in QMC. The procedure involves inferring long-range amplitudes in the wave function from integrals over the small region where all the particles interact. Evaluating the integrals using the energy information from Green's function Monte Carlo reproduces existing results in neutron scattering from He-4, and the phase shifts are unbiased by the method's regularization parameter. This technique makes a path for GFMC-accurate calculations of coupled-channel scattering and, with further work reactions, in nuclear mass ranges that may be permanently beyond the range of the other few-body methods