First, there is software readily available for tracking the moon, even control the two rotors to control azimuth and elevation of the antenna array based upon known moon orbital parameters. Problem is to find those new parameters. It turns out not to be all that hard.
A system designed for moon bounce is working with such small signals that when working with signal to noise ratio, noise is measured is degrees kelvin instead of the usual micro volts. The noise comes from a number of sources, among them the receiver itself, feed line, antenna generated noise, noise originating with the sun and reflected off water vapor in the air, etc. When calibrating such a system, one points the antenna at the cool earth and notes the noise, then the sun, noting the noise, then clear sky, noting the noise, etc. When the antenna points at the moon there is a clearly detectable noise (all this being white noise). Some of these tracking software actually use algorithms similar to military aircraft weapon search patterns, there are a number of them. Anyway, using a search pattern, the moon can be readily found, even on an overcast evening. By plotting a number of points found in this way, the new orbital parameters of the moon can be calculated.
It also occurs to me that we should be able to use the difference between the current obit parameters of the moon and the new ones we get by finding it's new ones, we could calculate the actual change that occurs during the pole shift. That is, if the moon's orbit isn't perturbed by the 12th's passing, which it seems that it would.
Offered by Ron.