OK, with the work that was done it tells me it might have run OK sometime before the head was taken off.
I don't think the phasers go bad but I never talked to anyone read about them going bad. I saw videos of them being taken apart and they look like should be OK with just some cleaning or flushing of some type.
There is a tool kit to reestablish the proper positions of each camshaft when the engine goes back together. How did you determine the camshaft along with the crankshaft positions are correct?
I read some place that if the cam sprockets are off more than 1 1/2 degrees from factory settings the car will show an error code. I am just guessing, but if the cam sprocket sensors are installed in a little different position or angle, this could trigger a code. Would the engine still run OR fail to run, I don't know. I have read just removing and reinstalling the same crankshaft sensor requires a special tool (Tech-2 or similar diagnostic device) relearn procedure.
In my opinion being 1 1/2 degrees is so little I wouldn't know how to measure it. That is too technical for me with the tools I have. I suppose with one of the high priced diagnostic readers, it might be something that can be measured or recorded. It also could be something for a "re-learn" procedure. Not having some of the pricy diagnostic tools is a road block. One thing you might do is to do a cranking compression test.
I changed the timing belt on my 2008, checked the timing marks 4 or more times a couple of different ways and got 2 different codes the cam and crank shafts were not in time. I never touched the crankshaft sensor but I did unbolt the camshaft sensor when I changed the timing belt and related parts.
I worked and worked on things, looking for something I didn't do correctly. I re positioned the one and only camshaft sensor to the right and left ever so slightly (maybe a 32nd of an inch) until the engine didn't buck at low RPM and moderate acceleration. The engine runs fine now but I still have a code every now and then. On a 2008, messing with the crankshaft sensor requires a relearn. Supposed no relearn is required for a camshaft sensor BUT I suspect it does require something like a re-learn with the Tech-2 or similar diagnostic tool.
FYI The chart or list you post #2 is too small for me to read and even after I copy it, and enlarging it makes it unreadable.
Does the engine run and how well?