When I ride fixed, the thought of pedal strike is so ingrained in my head (luckily it's never happened), that I always take turns less aggressively then on my road bike - which I bank like mad. So there's no doubt the experience will give you the same mindset, which should alter your behavior.

On the clearance side of things... I find that the pedal makes a major difference... as mentioned above, a shorter crank helps a bit - but if you save 5mm on the crank, it might not make as much a difference as getting a short track pedal - so I would look at your pedal first. Lead your bike over with the crank arm down and see how much bank you have - then put a track pedal on and see the difference.