have you changed the thrust arm bushings. the wider grippier tire will make the shake more noticable. i had to replace mine 4 months ago. i replaced the thrust arms with the 750il bushings (they are heavier), tie-rods, & center link. the mechanic that aligned the car told me my 540i was one of the tightest front ends he ever worked on.
tim s.
1995 540i/a
1987 325e