Owen, I love those old school learning techniques--I feel like I'm still missing some of those fundamentals even though I've gotten to try lots of things that would not have been practical even 15 years ago. I may just get out my tripod and a toilet paper tube tomorrow afternoon...
Antoine, if you have a camera (even an old still camera), a tripod, and a cat (or another object that moves around in unpredictable ways), tracking with it on a long lens will help you develop an instinct for how fast to track a subject at various speeds. Likewise for pulling focus on your own... I did this in my apartment in college, so the risk of arrest is slightly reduced.
I try to concentrate on the subject, without overthinking what *I'm* doing. With practice, and familiarity with the gear, your muscles will remember how to move. Very zen. The idea is to anticipate, rather than respond to the subject's movement. Your brain can subconciously recognize the minute body language that says the subject is about to stand up, shift their weight, etc. Getting rehearsals for difficult moves is helpful too--I'm sure some masters can nail anything cold, but not me.
I think your jerky or mechanical movements may be due to overthinking your own motions, or overreacting when trying to catch up with a subject. Or a sticky friction head.