Reading your description of your problem, I wonder if it isn't more of an issue with dealing with stress rather than developing a time management strategy. It sounds like that at least during the middle section of the test you find yourself able to get through questions at a steady pace.
The way I try to approach things, test time management requires a strategy to allot time for each question and then stress management to ensure the strategy can be implemented. If your challenge is getting yourself going at the beginning, and then keeping your pace as time begins to run down, you may want to look into different stress management or relaxation techniques. There are many things you could try that would not disturb others. I like to use deep breathing. There are also things like mini-massage or muscle contraction-and-release. Most of those strategies also involve positive thinking. You need to imagine yourself out of the stressful situation.
There are differnent approaches for all of these, so I would recommending searching online until you find an approach that makes sense. Also, remember that while you may need to spend some time, you could end up netting an additional few minutes by being more relaxed overall. And finally, you may find that all of the strategies seem a little silly. Remember, though, that stress is physiological. So even if you don't believe that changing your breathing will do anything, you can still benefit by going through the motions.
Good luck.