How many miles on the car? How long have you owned the car?
You mention misfire. If you have a random misfire you should get a MIL light with a P300 code. That would be followed by a P030N code where N is the cylinder. Your problem does not appear to be a misfire.
Take a look at the Idle Issues Thread I created. A couple of other things:
- Get a cheap stethoscope and listen to each of the fuel injectors as you rotate the throttle. You should hear a consistent clicking pattern on each cylinder. If you don’t, report back.
- Remove & clean the EGR Valve and EGR Sensor.
- Did you remove the throttle body to clean it? Look at the idle thread where I found damage to the bellows that goes on the throttle body.
- If that stepper motor is original - consider changing it. The SNG aftermarket one is good and inexpensive. My experience is it is impossible to test.
- When you turn the ignition key on (engine off) does the MIL light come on? i.e. is the bulb working?
- When you start the car does the secondary air system come on briefly?
Btw - if your car is a 3.0 that could be the problem. You’ve lost a cylinder. Most AJ16s are 4.0s…just Kidding. 
PS. CPS only affects starting - Hmmm - Not my experience. But should not be your problem as it sounds like an idle issue.