The most likely thing is still an air leak(s) somewhere. You say that it's expected that the engine runs rough with the oil cap off but it for sure is going to run rough if the CCV valve is shot so that isn't ruled out. I no longer have the CCV so I can't speak to what the crankcase vacuum should be if it is working correctly. With that many miles ( I have 450k kms) there is probably more than one thing going on as well. I know both my rear main seal and pan gasket are leaking air into the crankcase, my injectors are leaky, and my cats are probably not the greatest so I'm always on the edge of having the CEL come on/off. I can get my light out with engine oil stop leak, a can of cat cleaner, or boosting the fuel pressure a bit but none of that is consistent and that isn't really a fix.

If you haven't checked your fuel pressure driving under load you should do that as well.

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