If the problem is only at idle and you ruled out everything else it's likely that a valve is not opening enough, (especially with that engine asfaik) so that is what you should be looking at, and for something that would cause that, especially now with the engine apart.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)