Moons embedded in gaps within Saturn's main rings generate waves on the gap edges due to their gravitational disturbances. These edge waves can serve as diagnostics for the masses and, in some cases, orbital characteristics of the embedded moons. Although N-body simulations of the edges are far better in inferring masses from edge morphology, the long run-times of this technique often make it impractical. In this paper, we describe a faster approach to narrow the range of masses to explore with N-body simulations, to explore the multidimensional parameter space of edge/moon interactions, and to guide the planning of spacecraft observations. Using numerical, test-particle models and neglecting particle-particle interactions, we demonstrate that the simple analytic theory of the edge waves applies well to Pan in the Encke Gap but breaks down for smaller moons/gaps like Daphnis in the Keeler Gap. Fitting an analytic model to our simulation results allows us to suggest an improved relationship between moon-mass and edge wave amplitude. Numerical methods also grant freedom to explore a wider range of moon and ring orbits than the circular, coplanar case considered by analytic theory. We examine how pre-encounter inclinations and eccentricities affect the properties of the edge waves. In the case where the moon or ring-edge particle orbits initially have eccentric radial variations that are large compared to the gap width, there is considerable variation in edge wave amplitude depending on the orbital phase of the encounter. Inclined moons also affect the edge wave amplitude, potentially significantly, as well as generate vertical waves on the gap-edges. Recent Cassini images acquired as Saturn approaches equinox and the Sun's elevation on the ringplane is extremely low have revealed long shadows associated with the Keeler gap edge waves created by the embedded moon Daphnis. We interpret these as being cast by ~1 km high vertical structure in the waves created by Daphnis' out-of-plane perturbations on the ring particles.