We provide a detailed statistical study of the ejection of fictitious Earth-mass planets from the habitable zones of the solar twins HD 20782 and HD 188015. These systems possess a giant planet that crosses into the stellar habitable zone, thus effectively thwarting the possibility of habitable terrestrial planets. In the case of HD 188015, the orbit of the giant planet is essentially circular, whereas in the case of HD 20782, it is extremely elliptical. As starting positions for the giant planets, we consider both the apogee and perigee positions, whereas the starting positions of the Earth-mass planets are widely varied. For the giant planets, we consider models based on their minimum masses as well as models where the masses are increased by 30%. Our simulations indicate a large range of statistical properties concerning the ejection of the Earth-mass planets from the stellar habitable zones. For example, it is found that the ejection times for the Earth-mass planets from the habitable zones of HD 20782 and HD 188015, originally placed at the centre of the habitable zones, vary by a factor of ~200 and ~1500, respectively, depending on the starting positions of the giant and terrestrial planets. If the mass of the giant planet is increased by 30%, the variation in ejection time for HD 188015 increases to a factor of ~6000. However, the short survival times of any Earth-mass planets in these systems are of no surprise. It is noteworthy, however, that considerable differences in the survival times of the Earth-mass planets are found, which may be relevant for establishing guidelines of stability for systems with less intrusive giant planets.