Writing faster literally just comes with practice. If you want to increase the speed in which you can think and transcribe on to paper, just practice writing. Obviously, it makes the most sense to suggest you write analyses in your own time, but you don't even necessarily have to do that in order to get your hand flowing over paper. The challenge is though is keeping cogent thoughts with legible handwriting. Again, this just takes practice.
Reading other exemplar practice essays is a very passive form of learning. I'm not saying that reading top-scoring essays wouldn't help you to improve your writing, but it is far more practical to do writing yourself. I believe that reading examples should only really be used if you want to compare writing styles or look specifically what differentiates your form of writing with those of the top band. However, that is just my opinion.
For me last year, I decided just to watch a few films and TV shows and decided to take notes and analyse them for fun. I suggest attempting this over the holidays at least once to at least see if this would be beneficial for you. I know for myself, that was a good training exercise in being more perceptive in picking up details, explaining what they are and interpreting the purpose of them.