I learned early on autoxing that you can't overdrive the car and expect fast times - especially a heavy car such as a BMW.
The best advice I was ever given was the come into a corner faster, brake less, and get on the throttle later - just let the chassis and tires take the grip around the corner. I dropped a massive amount of time.
Coming into autox from a largely track background, my mentality had always been to set the car into the turn and get back on the throttle as soon as possible. With autox, I couldn't do that. When I first started I became very frustrated until a very experienced autocrosser noticed how I was driving - I was somehow able to get a supercharged s2000 I was co-driving to understeer. Imagine that. He gave me the advice I posted above and man, did it make a huge difference.
Before messing with tire pressures, id modify my driving to see if it helps at all. When you change too many variables, you never know exactly what fixed the issue - and then you don't learn for the next time you have a handling issue.