Your issues are quite common to most test takers studying for this exam.

For your issue of getting directly into solution and not thinking about the problem first I highly recommend you keep a question log for every question that you do. In the log write down what category each problem is and the most efficient way to solve the problem. This awareness should start to creep into your test taking. In addition I have all of my students identify the problem type before starting each problem. This may help you.

As far as the two minute deadline, that is an average and it would be best to not think of it as 2 minutes per question but more of an average. There are some problems that can be solved much faster and some that take longer. I suggest looking at each problem and asking yourself if you can solve that problem in 3 minutes (not 2). If you think you can then you should give it all you have, if you think it will take you longer than three minutes then it may be a good problem to skip to give yourself more time on future problems and thereby maximize your score.

You issue of not thinking of alternate numbers can also be addressed by a question log - keeping in mind what you should have thought of and idenitifying the language that indicates those numbers. If you can see them after teh fact then it is more about calming down and not stressing during the exam.

Best of Luck