this shift manages to capture 6 more hits, apparently not losing any, at the cost of an additional rule bringing a new factor (perigee) and an arbitrary number (3 days). Is there at least symmetry so that the window also slides back if perigee is AFTER syzygy, or would that produce inconvenient results?

This sounds like a prime example of tuning the method after the fact, then testing it as though it was a prediction, and not even counting the free parameters used to achieve the fit.