I find it most comfortable to think in terms of syllables, not words and letters. Then again, I'm not getting any faster no matter how many tests I do so maybe I need a change of strategy.

Good point, mate. But here's why your're wrong:
You know how when you start reading you HAVE to think about each letter individually? But then you start learning how specific words look like on the page, so as you get better at reading you don't look at the whole word as much as you recognize its image.

It's the same in typing, only instead of reading, you're moving your fingers. At first you have to pay attention to each keystroke, but as time goes on and you internalize the movement of the keystroke, you also internalize the sequence of keystrokes associated to specific words.... So you no longer think about each keystroke individually.
Of course, the only way to do that is to mindfully practice the sequence until it's etched into your muscle memory. That means practicing slowly, and very intentionally.

Good quote, and an excellent point.