A paramount goal in nuclear physics is to unify ab-initio treatments of bound and unboundstates. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here I introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC, implement it numerically in the definitive computer codes for these methods, and test it out in nuclear systems small enough for quick turnaround but large enough to have interesting dynamics. The method involves inferring long-range amplitudes in the wave function from integrals over the small region where all the particles interact. This approach using integral relations is well established in the literature; here, I develop it for the QMC framework in both variational Monte Carlo (VMC) and Green’s function Monte Carlo (GFMC) calculations. The integral method produces more accurate scattering observables in neutron-3H scattering for VMC wave functions than direct evaluation from the same variational wave function. Applying the integral method in Green’s function Monte Carlo reproduces existing results in neutron-alpha scattering, clearing the way for its use in coupled-channels problems. Establishing these methods reduces the amount of human effort needed for a specified level of precision. It clears the way for GFMC-accurate calculations of coupled-channels scattering, including reactions, in nuclear mass ranges that may be permanently beyond the range of the other few-body methods.