Fixing leg position while turning
Assuming you don't have fixed gears, i.e. the wheel can roll forwards without the pedals turning, the best way to corner is with the outside foot down, and weight on that foot. The thing is that you don't have to hold this (outside foot down) position for more than a few seconds per corner. If you can pedal without trouble you should be able to hold it briefly without trouble. And actually if you're cornering at modest speeds you can hold your pedals with the cranks horizontal and avoid the ground.

I suspect that your comfortable coasting position is mostly a learned habit - I know that I habitually unweight the saddle for bumpy descents with my right foot back, for example, and don't even notice for a few minutes. A conscious effort to hold a more appropriate position is worth trying before anything else - that would be a useful start even if you do find you have to do something else.