If the tranny slip light has not come on it is not a band or broken component problem. I think you will find it will be a selector / valve body/ solenoid / 'o' ring issue. You need a tranny specialist rather than a BMW specialist. Most stealers don't seem to be either one of those.....
Good - Fast - Cheap: Pick any two.
E23 735i; E30 318i; E32 735iL (X 2 - 1 White and 1 Light Blue); E34 535i; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i