I have to ask if the engine oil level was checked regularly, in between the regularly scheduled oil changes? A lot of folks don't know that the 5.6 motor, being a DI engine uses oil laden air blowby through the PCV valves to lubricate the valve guide rods. I had no idea about this when I first bought by '12 M56x back in September '15. I checked it after I got it home, and didn't check it again until the next oil change. I pulled the dipstick and it was bone dry - holy crap I almost passed out. No leaks anywhere, so I researched and found out that you have to add oil in between changes. Doesn't matter what type or brand, it'll use it just the same (my experience, and I tried different types). The timing chain recall mentioned was started because of a faulty oil jet or jets that caused premature timing chain wear. My car started running rough like yours on the way home from work one day, and I was able to make it to the dealership. At that time they had just started the recall campaign, and they took me right in and gave me a loaner Q70L to drive around while the work was being done. Refer to this document that details the scope of the labor and parts/fluids replaced at no cost to you:
https://static.nhtsa.gov/odi/tsbs/2016/ ... 1-2280.pdf
This is a very extensive job - they had my car for a week. Some folks may have had theirs done quicker I don't know. I would think that you would remember this particular recall work if you had it done. If the oil jet failed the hole fit test they're supposed to replace the engine.
Now I check my oil levels a couple of times in between changes. As long as it's in between the holes, I'm good.