Drew - FWIW, I had that wire to the oil level sensor all the way removed when I had the fuel rail off for the V-pan repair. What I noticed is that the wire is in a fairly precarious position on the front of the engine clipped in behind the vibration damper and then snakes past the AC pump and on to the sump parting company with the starter motor wires somewhere underneath IIRC. The wire runs from the wiring box on top of the P/side valve cover and passes under the air intake elbow. On mine the plastic cover was falling apart in a few places and I put some black electrical tape to protect it.

This is all quite difficult to see without removing the front cover between the stiffener plate and the stiffener plate itself. Then reaching in there is hardly a clean job.....but if I had to guess I'd say it might be a wiring issue. I'd start from there as it is the easier thing to ascertain and cheapest to fix.

BTW, you are right on the oil volume, I always start with 6 qts and then run, let settle and start adding 1/2 qts until halfway between E and F on the dipstick. It is about 8 and change in total.

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2003 4.4i black ext./black int./black headliner (kid's runabout)
2014 535d X-drive, M package, silver/black interior

Sold but not forgotten:
2009 E70 35d, black ext./black int./black headliner (sold 2021)
2006 4.8iS Le Mans blue/cream int./black headliner, SOLD in 2012 sadly...

Other hardware:
2015 Cayenne S (wife's new DD and definitely wroooommmmm)
2016 Tundra 1794 edition crew cab, luxo hauler
2005 Tundra crew cab, weekend hauler. Sold after 150k very happy miles.