One major advantage of the magnet is that if he does test well he is going to get a spot...can you imagine how you would feel if he qualified and then lost the lottery.
Even though the test underestimated your dd it isn't correct to say 'a few more wrong answers and she woulntt have made it' rather I would recommend to train yourself to think: Although these tests are far from perfect they are usually accurate and when they are off they are usually only a little off. So the odds of the test being way way off are quite small.
If that rare even does occur I don't think changing schools is going to be damaging. As time goes by you will learn more and understand things better and it might be fairly easy. Or perhaps you'll get lucky and a whole cohort of younger siblings of gifted kids will be in K with your son at the magnet and they will be lifelong friends. Or maybe you'll homeschool by then. Or maybe they will allow him to retest the year after. Or maybe dd will be miserable and need a change by then anyway. Or maybe....
Play the odds. Save wear and tear on yourself. Use the time to bring them to chess club on the weekends or just have fun.
Hope that helps and doesn't sound flip. You do have legitimate cause to worry but I sense that the cure is more costly than the disease. We adult gifties try and use our heightened sensitivities to avoid every peril and then our imaginations might make the peril seem even more perilous. This is a very hard parenting skill to learn and it takes making a few mistakes. But yes I do smell perfectionism at work here. You shouldn't have so few good options. It isn't fair. It isn't right. But your family will find a way to manage. You will.
Love and more love
Grinity