As Bruce noted earlier the reason for having the left side long is that torque will tend to lift the left wheel at the hit and thus having the right wheel trailing will blank the beam for a longer period of time. If you are running something like a J/D that does not carry the front end leaving then the difference is academic but for all others having the left lead is beneficial. As for the car turning left better with the right wheel leading, that sounds more like an ackerman issue as the location of the contact patch should not have any affect at slow turnout speeds. A lot of juniors have funky scrub radius geometry too and that will accentuate the problem.
Roo