Please help me fix my car

[ziomekpl18]

Hey guys, I need your help, my car is a 2012 A6 with 125k miles. My problems started on a 1000mile road trip. Before that road trip I changed oil and filter but I was in hurry and forgot to tighten the oil filter housing (very rookie mistake, I know). Drove like that around 300 miles, then noticed smoke behind my car, I pulled over, smelled burnt oil and tighten the oil filter, it was dripping on the cats, I then added around 2qt of oil on the next gas station and then again 3qt of oil (I didn't know how much oil I have lost, so had to keep adding until it was ok). After the trip codes showed up for timing. P0011 P0016 etc. out of corelation. so I said to myself ok I screwed up it is time to be a man and pay for this. so I took my car to a known Audi mechanic(very good and honest guy), he did the WHOLE timing job ,replaced all my timing components, chains, guides, tensioners, rear main seal, bolts, both camshaft sensors, crankshaft sensor, both camshaft adjuster sprockets and both camshaft adjuster solenoids (N205), and flushed the engine twice, because there was some metal shavings in the oil, now its clean after 3-4 oil changes (LQ Molygen 5W40) since I saw them. Now car starts and drives like new (there was 1-2 seconds of chain rattle before timing job) and all is good, timing marks are dead spot on. He already checked it twice again. HOWEVER EVERY COLD START (only on cold start) THE CAR IS THROWING CODE P0052A (timing over advanced) and sometimes P0011 and is in limp mode, I have to delete them everyday as it is my daily car. Also tried contacting 034(car is stg2+ with all supported mods) if they can delete that code for me but they said NO :( .
What should I do ? Is something else damaged from lack of oil on that trip? Bearings? or still something with timing? I'm running out of ideas now, and money soon

[LowKeyLoki]

Metal shavings in oil = very bad sign. Sorry to say but you may have ruined several bearings on your crankshaft. If you were 2-3 or more quarts low while driving that is A LOT! I’d have the compression checked on each cylinder and if they’re ok just keep driving and hope for the best.

[Benji16]

I got a whole motor for sale if you need it.

[LYKUNO]

Just found an interesting video by the HumbleMechanic: "Seized 3.0 Supercharged Audi Engine ~ Complete Engine Failure". In the video he performs a complete teardown of the engine, and reveals the cause of the catastrophic failure. the video also reveals the complexity of the engine and ancillary components and is compelling to watch in its entirety.

One of the commentors had this to say: "We've replaced 3 of these engines in the last two years in our small VAG only shop. 2 locked up solid, 1 let rods out in spectacular fashion, but they all had seized rod bearings. Rods out had 42k miles, bought new, never tuned. First seized had 152k miles, dual pulley with tuning. In the end we traced all 3 back to the HPFPs leaking gasoline into the engine oil. We pay very close attention to the smell of the oil when doing oil changes on these engines now."