Quick answer.......
Yes, you can throw CEL's "that quickly".
Those rubber boots are a PITA and I had a couple that were (as you described) in that condition when I swapped plugs myself. It appeared they were like that from the factory. Strange huh?
As far as getting it into Neutral (without starting/running the car) I have pressed and held the Start button, so that the car simply goes into full 'ON' mode (but be sure NOT to press the brake).
Once you've done the above, then, without any further depression of the Start button, simply press you foot on the brake pedal, to move it into w/e gear position you desire.
Once you've physically pushed the vehicle to wherever, then place the gear selector back into Park, foot off the brake, then press the Start button to get car back out of 'ON' mode.
As far as the codes, not sure

But that gets 'ya 75% of the way there.