About a month ago I was in your exact situation. I thought the whole "slow down to speed up" advice was cliche and wouldn't work if I was already running out of time. So I tried it, and it did help. I drastically reduced the number of questions I missed for carelessness (ie. I was going to fast and didn't bother to read all of the answers.) It actually slows you down if you try to go to fast because you end up having to go back and read through the question again two or three times.
Take it or leave it, but here's my advice. First, read each question thoroughly, don't speed read, as you might miss something. Think about what you're reading and what the question is asking. A lot of the time, you'll be able to guess the answer. Second, remember that there is a right answer. A lot of my mistakes were because I thought I had found a "good" answer, and didn't bother to find the right one. I think doing that also significantly dropped the number of carelessness mistakes I made.
You probably don't want to hear about changing you mindset, but that helps as well. Being confident in such a way that you know that you can find the right answer helps a lot. It's not "I know I'm going to ace this" but that "I know I'm good enough to find the right answer."
Anyway, back to your problem, it really does sound like you need to not worry so much about how long you're taking. Don't worry so much about how long it takes to read the questions, and when you have found the right answer don't dwell on it for a long time. Hope some of that helped.