Very impressive write-up. Writers are generally quick to state the first part of the Scheimpflug rule (film plane, lens plane, and plane of focus converge) but tend to ignore the more complicated second part (plane of focus, front focal plane, and parallel-to-film lens plane converge), and the rather complicated relationships of how these converging planes actually interact.
I agree with Dave that for field work an empirical, iterative approach is more suitable than using a theoretical approach trying to compute the required tilt.
For a given scene, I decide whether a tilted plane of focus (generally, horizontal plane tilted upwards) would be advantageous (needed) or not. Select a close point and far point (objects in the scene) of the desired plane of focus, start with some tilt, focus on one of the two points. If the other point is also in focus, the amount of tilt applied is correct; but if in order to get the other point into focus need focusing movement towards the tilt (suggesting not enough tilt) or focusing movement away from the tilt (suggesting too much tilt) [hope I got this the right way round!]. Adjust tilt accordingly, and repeat until both points are together in focus. Check whether objects outside the plane of focus are sufficiently in focus (or out of focus, if this is desired). If not, try a slightly different plane of focus, and repeat.