"I have found that on flats when I need to catch someone's wheel or something I frequently shift into an easier gear to speed up - which obviously does not make too much sense, but seems to work."
That makes perfect sense, because for the same effort on the pedals, the easier gear will let you accelerate faster and the higher-RPMs will give you more power. Just that your heart-rate may be a little higher than using a bigger gear, but that will end up hurting your legs more. It's all a balancing act.
As for bouncing, test your spin-stroke by doing 5-10 revolutions slowly with one leg at a time. Also ride more rollers...