Good observation on the gear oil smell. It's distinctly different from the engine oil it just seemed like there is a lot of oil on the diff case.

Oil filter cap leak makes a disaster off the whole front of the engine so that's not likely the source.

Outside the box thinking:

Seal at the bottom of the dipstick tube?

CCV tubing/ intake (should not have that much oil going though but if something is amiss and there is too much crankcase vacuum it can pull oil where doesn't belong.

Open your oil fill cap when running and see if there's a ton of vacuum.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)