What should be done if evaluation shows that a neighbor might experience more than the allowable limit of RF exposure from the main lobe of a directional antenna?
Why RF exposure from a beam is highest in the main lobe, so the practical fix is to control where that lobe points. If a routine evaluation shows a neighbor could exceed the MPE limit, you must limit exposure, for example by restricting antenna rotation so the main lobe never sweeps an occupied area, or by reducing power or duty cycle. The rules require you to ensure no one is exposed above the limits, and mechanical or operational controls on pointing are an accepted way to do that.
Watch out A higher front-to-back ratio only reduces radiation off the back of the antenna, which does nothing about the main lobe aimed at the neighbor, and "non-polarized" antennas with higher gain would only increase the field strength in the main lobe.
The main lobe is the problem, so aim it away. Extra gain or better F/B never fixes what's in front of the beam.