Hi, as a psychologist, I would recommend that you get accommodations via ADA. I think in order to do that, you need a report from a psychologist with your diagnosis and recommendations regarding this requirement of tests. It may be that you get twice the amount of time to accomplish it. What else do you think would help? In what area are you? State, city. I can help you find someone to do it. Or, can you go to the person who diagnosed your daughter?
This issue is going to keep coming up in many areas when you need a test of some kind. Not just at work. Even if you changed jobs this could happen again. So, I think it is worth it.
Also, because it is the perception of a time limit that bothers you, and the fact that you could lose your job if you don’t pass, I would highly recommend looking at changing the pressure on yourself. Change your own perception. Visualize yourself doing it well and on time. As you said, you could ace it. Take the time limit off of yourself. It is just a matter of perception. Easier said than done, I know. Some test taking guided imagery apps might help.