My handwriting was terrible -- until I took a technical drafting course in school. The two things I got out of it that lasted were readable handwriting and better arrowheads on lines, when I remember to do them properly.

Good news: you don't actually have to take a technical drafting course. You just need to find an architectural lettering guide that you like, and practice for about fifteen minutes a day until it feels normal. (Architectural, not ASME. ASME is too rigorous to become anyone's daily handwriting.)