The problem you are discussing is called tramming or tracking.
Try this tire trick.
-Add 2 psi to your front tires > Change? Y/N?
-Reduce your tire pressure 2 psi > Change Y/N?

Post your results. It may take 4 psi depending on your actual running tire PSI. Some brands/models are a lot more sensitive to tracking than other brands. Side wall and shoulder construction material and designs are the reasons. All can be minimized with pressure changes assuming that the front end parts are within tolerances.

Question on your 4.4:
Which tire size and brand are you running?
Are they the same size and brands on all four corners?
What is the PSI cold reading on all FOUR tires now?

If you are stopped and the engine is off, is there play in your steering wheel (left to right)BEFORE the tires actually move?

Helpful?

__________________

2005 X5 4.8IS
The Blue ones are always FASTER....

Current Garage:
2005 X5 4.8is
2002 M5 TiSilver
2003 525iT
1998 528i
Former Garage Stable Highlights
2004 325XiT Sport
1973 De Tomaso Pantera, L Model
1970 Dodge Challenger T/A 4 sp Alpine White
1970 Dodge Challenger T/A 4 sp GoManGo Green
1971 Dart Sport, “Dart Light” package
1969 Road Runner 383
1968 Ply Barracuda 340S FB Sea-foam Green