2006 Mazda 3 2.3l stalling/rough idle in D & R after TCM replacement P0011 P0016
I replaced the TCM (Transmission Control Module) a few weeks ago after having heavy slams putting the car into reverse and being stuck in limp mode. I initially replaced the transmission mount but that didn't fix it so I ordered a TCM. The TCM replacement appeared to fix the issue and I was able to drive the car for a day (40 minute mostly highway drive) with normal shifting and running. However, when I went home later that day I noticed the car's idle was rough. The car made it to the highway and all the way 30+ miles on the highway with no issues but when I got off the highway it almost stalled at a stopsign. Eventually five minutes from home after a few more near-stalls the car did stall on the side of the road and the CEL came up with a P0011 and P0016. I could not get the car to start for several minutes. Once I finally got it to start I was able to barely get it home and immediately upon pulling in my slightly-inclined driveway and slowing down to a near-stop the car stalled out again.
Since then I have let the car idle for 20 minutes and then 20 more with the A/C on full blast as I read to do after any long term battery disconnection to reset the idle as the battery was disconnected for several days before I got the new TCM in. I did this twice and it made no difference. I also replaced the VVT solenoid under the valve cover gasket and replaced the spark plugs which looked pretty bad. The timing chain looked good with good tension when I had the valve cover off but I didn't check it too thoroughly. I also didn't check the camshaft's for proper timing as I should have as I was hoping it was the VVT solenoid, an issue that I had read about from other drivers online. The car has been burning a lot oil for several years and I'm not super diligent about keeping it completely full. During oil changes it is often a quart low. I've read a few accounts that this could mean the PCV is clogged (I heard it's a PITA to get to) and I've read that it could also point to the timing chain jumping a tooth due to low oil/low oil pressure.
I've found a few drivers who said retiming the camshaft(s) fixed their similar issue, others have mentioned to replace the evap solenoid, some have said a throttle body cleaning fixed the issue, some say MAF clean/replacement, and I've seen O2 sensors be the culprit (I did have pending exhaust O2 sensor code briefly but it went away).
What is the best order or steps to diagnose this issue further? The engine/car runs great as long as you are not idling. If I rev the motor it runs perfectly with no misfires and if I am driving it drives great until I come to a stop. It idles poorly in Park but will stay running, in Reverse the idle gets worse with lots of surges, and even worse in Drive where it will usually stall.