loyalgargoyle

Hey everyone, I'm new here. I'm here because I have a frustrating idle problem. I have googled the problem many times, and I can't find anything.

So here's the problem. I will try to add all possibly relevant information. Sorry for everything that follows, but hopefully all the information will help narrow down what the problem(s) are.
I have a 2002 Honda Accord V6, around 270k miles. The car used to have a worse idle problem before, typical idle fluctuation. I fixed a vacuum leak, replaced the IACV twice, PCV valve, adjusted the base idle. The idle no longer fluctuates, but the idle does surge when the car is slowing down between the last two downshifts. It is worst when shifting to first gear right before coming to a stop. The idle also surges when putting the car in park, but will usually come back down to around 700 after a few seconds. When I say 'surge', the idle is not fluctuating. It just rises up to around 1200ish maybe? If I brake very hard when coming to a stop, it will skip the surge from 2nd to 1st. So the 'amount of surge' increases if I am coming to a stop slowly.

The car is not throwing any idle related codes. It is throwing the EGR code and P0420. The downstream 02 sensor has been replaced, but it also was throwing a code specifically for that sensor before it was replaced. Perhaps the upstream sensor is bad and causing the issue, but it isn't throwing an upstream 02 sensor specific code?
If the car is idling for a little bit, there will be an occasional tick that brings the idle a tad bit lower, pretty sure this is normal, but when it happens, the headlights dim briefly. Wondering if bad grounds could maybe be another suspect of the problem. Sometimes the CEL light flickers a little bit while idling.

One other thing that makes me wonder if it's ground/alternator related is because after driving it for a bit, there will be a sound from the stereo whose frequency will follow the RPM. This only happens after driving for maybe 25 minutes or so, but it will last the remainder of the trip. It won't go away unless I haven't driven for a few hours.
Also, I have heard that a bad alternator can throw false codes. The EGR code makes no sense because the EGR valve has been replaced and the passages have been cleaned.

RARELY, after starting the car, the idle will get very low and stumble. It will go back up after I touch the gas.
ALSO RARELY, the idle will softly fluctuate after putting the car in park.
Both of these two above problems don't happen very regularly.

The car also doesn't have much power. I figure this has to do with the p0420, clogged cat or bad 02 sensors.

Now, if I disconnect the battery for a few minutes to reset the cars computer, most of these problems go away. Let me explain what this looks like: I plug the batter up, and I drive. The idle will VERY SOFTLY surge between the last two downshifts when coming to a stop. So softly, it's barely noticeable, but you can see the RPM needle indicating it. The stereo does NOT have any noise following the RPM at all. The power seems to be a little bit better, and the idle doesn't feel so rough. After driving for about 30 minutes, the CEL and TPS will come on, usually when I'm stopped at a stop light. The noise that follows the RPM from the stereo usually starts about a minute after the CEL and TPS come back on. The surge between the downshifts when coming to a stop gets worse and is noticeable and obnoxious.
If I disconnect the battery, all of this will go away again, and this whole scenario will repeat itself.

I disconnect the battery almost every day before I go to work so I start the day without having to deal with these silly annoyances. But they will come back around half an hour of driving.

If any of that doesn't make sense, I apologize, I probably explained it poorly. Any and all help would be appreciated. I don't want to throw money in the wrong direction!
I can also record video of the problem if it would help.