This study presents advancements to a laminar-to-turbulent transition prediction technique based on the linear PSE3D framework. This method models disturbance propagation through genuinely three-dimensional compressible laminar boundary layers that form over complex wing surfaces. To account for streamwise and spanwise curvature, we first derive a simplified form of the Navier-Stokes equations in a general body-fitted non-orthogonal coordinate system. We then analyze the characteristics of the rapidly varying components of the PSE3D system and determine a second closure condition, both using ray-tracing. These rapidly varying characteristics will give the direction of propagation of the disturbance and inform improvements to a local point-to-point marching (PPM) scheme, which efficiently solves the PSE3D. The propagation direction obtained via ray-tracing provides further insight into computing the N-factor in an effectively two-dimensional manner across an entire three-dimensional varying surface. We describe this novel N-factor calculator and present various stability and N-factor computations conducted on the AFRL 1303 UCAV concept, comparing the outcomes when using line-of-flight, inviscid freestream, and group velocity as propagation directions.