the reason it's easier to lean left is because your throttle hand is not as confined. it is more relaxed when hanging off the left. as for tire sliding. i've only slid them on cold tires on a crappy cold moist morning on the first corner. i've slid them both many times on the track. that's when they have reach max temp and will start reducing traction on the next cool down cycle.
riding hard on low tire pressure sometimes feels like you are sliding both tires.
low tire pressure will also cook the tires.
Since you ride street most of the time, keep your knees tucked in when hanging off. get rear sets so you don't mess up your balance by moving your feet around from tip toe to gear changing. make a conscious effort to countersteer on high speed turns. this is where newbies panick and go off-roading.
an hour of track time = 1 year street riding experience.