None of the parts you listed will cause this problem. The engine Computer loses its memory when the battery is disconnected. It has to relearn "minimum throttle" before it will know when it has to be in control of idle speed. To meet the conditions for the relearn to take place, drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the pedals.

Does that make the overhead light flicker when idling or is it something else?

Flickering lights is not related. If the battery is nearing the end of its life expectancy, I'd look at that first. It is the key component in helping the voltage regulator maintain proper system voltage. Also check the ground strap between the engine and body, and the smaller negative battery cable that is bolted to the body to be sure they're clean and tight.

You may want to have the charging system load-tested. If the alternator has one bad diode, it will only be able to produce exactly one third of its rated capacity of typically around 90 to 120 amps. Also, "ripple" will be very high. Most professional testers measure ripple. If it is excessive, the voltage regulator will respond to those variations in voltage and try to adjust the alternator's output accordingly. That can result in bouncing voltage levels and flickering lights.

Sounds just like problems I was having. Was actually a simple fix.
On mine the Ignition Coil on cylinder 7 was not an OEM. It was causing so much Electrical Noise it was able to shut down the computer completely at times.

Most of the Time however It was displaying very odd behaviors which were sometimes repeatable sometimes not.I had even replaced the computer in hopes of fixing this. And all it was was a bad after-market ignition coil.

I suggest you take a look and see if you have any of these Crap coils? If so replace with OEM and you might be quite happy..

There is a youtube video out there somewhere detailing the process used to identify the problem. I just could not find it again.

Thank you for adding to this solution.