When my son was preparing for the CFA we looked at the different rules for each Academy, and thought that someone could possibly game the system. Although really there is no advantage, since the test is the same for all, and frankly, you are just as likely to get a PE teacher who is biased towards the candidate as any other source, and every Academy accepts a PE teacher to give the CFA.
My son was kind of stuck with only one PE teacher, who is a strict hard-A, but he knew that while he was training, so he practiced with perfect form on everything. But I am certain there can be a huge difference between different testers.
There are also other interpretation issues for the CFA that we weren't sure how the teacher would score. The bb throw: would he measure the total distance the ball went if it was not straight? My son's tester did not. He marked the line, and if it was on an angle, distance was lost. My son said it didn't really matter because he threw it pretty straight, but things like that can be relevant.
At this point of the process I would not rely on one Academy getting scores to another Academy. Everything goes way too slow in those offices. Even posting ACT scores that are sent to the schools takes forever. Just have the tester submit scores to each school.