There is an handwriting system which involves using one stroke for one sound. This should save a lot of writing as usually normal writing would need to use as many as four stroke to represent each letter:
So a really slick form of handwriting would use one stroke for one sound. Simple, but too difficult? Not necessarily. You just need to learn to hear the sounds that you use when speaking English so you can write them, and then learn some simple symbols to represent those sounds. Since you have been taught to pay attention to 26 letters and not the actual sounds of English, tuning in to speech sounds may take a little time, but can also be quite interesting and fun.
However this handwriting system is probably a bit complicated to learn but if you really need faster handwriting then this may able to help.