I think the testing shouldn't involve Astrologers or people choosing charts made by astrologers. If the thing we want to test is Astrology itself, that's not the way to go.
How about testing some of the core assumptions of Astrology. For instance, some of the planetary "transits" and their alleged influences.
Astrologers claim that some planetary "transits" do facilitate the occurrence of physical accidents (e.g. injuries involved), for instance a transit of Saturn opposed your natal Mars. This corresponds to the current planet Saturn passing on the sky over a position opposed to (= at 180º from) where Mars was in your natal chart. In fact, any Saturn-Natal Mars transits could be checked. The Saturn-conjunction-Natal Mars transit allegedly coincide not just with accidents, but in particular with bone injuries.
If such transits truly makes accidents more prone to happen, that could be verified with records from traumatology or ER departments in hospitals.
Check the birthcharts of all patients that were registered in that or those hospitals as having some fracture or cut related traumas, let's say any day during the year 2000. Compute the incidence or closeness of any Saturn--natal Mars transit for all those patients over that whole year.
Then choose any other set of people that are known to not have had any record of accidents/injuries that same year 2000. See if the incidence/closeness of Saturn--natal Mars for this other group is in any way significantly lower, or in any case different than the other group's. If it is about the same, then the observed data would not support any correlation between said transit and any injuries/accidents (weaking the case of Astrology, as far as that transit goes.)
Several other transits could be verified similarly, depending on their alleged influence.