This question could be translated to "How to eliminate my humanity?"
Not to put OP on the spot, but unfortunately, careless mistakes are a part of being human, and they're a part of the reason why we'll never be fully prepared for a test like this. The fact that your brain is at maximum for three hours and some just means it's going to get tired and worst of all, you may not know when you make a mistake until after.
But you can greatly minimize them by eating properly and taking breaks. In my studying I learned that sometimes you burn out a little, but because you're so driven to improve and work harder, you don't even know it!
Also during your FLs, take a break before each passage. In my actual test, when I started the PS section, I clicked Start and just stopped for 10-15 seconds. My brain needed just a few seconds to accept and digest the fact that it was the real deal, and to do its best to translate the experience into a practice exam experience. Then, for each and every subsequent passage following, I took another 5-10 second break, and before starting the discretes, I did the same thing. Seems like a waste of time right? Turns out it only totaled to about a minute and a half. Also, when your brain is tired, it will relax, whether you want it to, know it, or not. It's just gonna happen. That means you're gonna get things wrong. Instead of letting it relax on its own, which is likely when you'll be working problems, why not chill out for a second so that you can go into each passage with maximum focus and energy?
