Practice makes perfect. Needs to get a natural instinctive style that is readable even when writing fast.
If this idea of thoughts running ahead has any validity, and not just an excuse, then maybe leaving out unnecessary words might help (except in an English exam of course). But again practice. Practice consciously holding the thought stream to a steady rate rather than concentrating all on this free flow of ideas leaving little for concentrating on putting the ideas down. Make mental priorities until the subconscious does it naturally.
My handwriting is hardly legible these days because almost every note is made on the computer not real pen & paper. I should also practice, but at my age it is hardly worthwhile for me any more.