I'm no expert typist and I can't speak to the OP's claims that a bump in typing speed translates to a corresponding increase in productivity, but I can attest to the fact that simple time spent practicing will improve your skills in almost anything, typing included. If you included a typing run at the beginning of your day and made sure you were using proper form, I think you might be surprised at how quickly and how drastically your typing speed might improve.

The key is simply sticking with it over the long term. A general rule I find rings true is that people tend to overestimate their improvement over a month, but underestimate improvement over a year.