Running rich with 2 different PCM's, Hmm. Lets break it down to what can cause it to be rich and tests to perform, May need help from the 2.9l guru's here though as I may miss something or don't know how to perform certain tests. I will edit this post to reflect correct info so it can be used in the future.
Rich on one bank Causes:
Miss Firing - this would explain the rough idle / intermittent miss fire at low RPM's / would cause O2's to read rich on that bank
Leaky Injector - this would allow fuel to enter the combustion chamber even when the injector is supposed to be closed.
Leaky Fuel Pressure Regulator - This would allow fuel to enter the vacuum system and enter the engine but Wouldn't this cause a rich situation on both banks? Maybe where the vacuum line connects to the engine is on the bank 1 side of the intake richening that one side?
Bad Upstream O2 Sensor or Reading - The O2's give the PCM a signal to calculate AFR. If the reading is not correct then it could throw the AFR off on that bank once the PCM runs out of fuel trim. Could have bad wire to PCM though. Can cause rough idle as you know and replaced it already.
Bad PCM - you have already ruled this one out with a different PCM and still have the issue.
Am I missing any thing else that can cause a rich condition?
So we are down to Spark And Fuel. One is off causing the issue so how to go about finding which one:
FUEL Delivery
2.9 Guru's, Does the fuel shut off with the gas peddle pressed all the way when cranking, clear flooded engine mode? If it does, You can press the peddle to the floor to shut the fuel off and crank the engine. IF it pops then you have a leaky injector. This is by far the easiest test and why I mention it first.
If you have access to a flow meter you can pressurize the injectors and see if they drip. You can also, If the fuel rail allows, pull all injectors out and leave them connected to the fuel rail and turn the key to Run. Be aware that the injectors may fire but usually only when cranking so only use the key to run position. Wipe the injector ends to be sure they are dry and watch for a drip. Be sure you keep the fuel rail pressurized and don't have a lot of bleed off right away. Fuel pressure gauge will be handy for this test.
IF the FPR (Fuel Pressure Regulator) is leaking fuel into the vacuum system you should be able to pull the vacuum hose off and see moisture in the line at the FPR. This is the sign it has gone bad and is leaking fuel into the vacuum system. This can happen and it still have the proper fuel pressure after the regulator. Simple test and also easy to perform.
Guru's Did miss anything?
SPARK Issues
Lets start at misfiring as this seems to me to be the more likely situation.
Pull the plugs on bank 1 and read them. The good thing is this is a pump gas engine so spark plugs don't take long to soot up and show how it is running. If one seems to be more carboned than the others you found which cylinder is misfiring. Be sure to look at the pericline inside of the glug also for signs of spark jumping to ground or extra sooty. This can go the other way also with all looking the same which could mean all three are getting extra fuel or no miss fire. With them out look at them carefully to see if the spark is shooting down the outside of the porcelain to ground. While this can be found other ways taking them out allows for you to see all around the plug and not have an obstructed view of part of it requiring a mirror causing poor visibility.
At night in a dark area with lights off start the engine and look closely at the wires looking for spark bleeding out to a ground. This could be anywhere in the ignition system from the coil all the way to each plug. A light mist of water in a spray bottle can sometimes help find it. You don't want to soak the wires just make it easier for the spark to jump to ground more consistently so just a light mist not leaving water drops on the wires and coil.
Check under the distributor cap for signs of spark traveling to a different post or down to the base of the cap. This will look like some one drew with a pencil a line between posts or down the side of the cap. The line may be jagged so look carefully.
Check the rotor also while here for abnormal ware and tare since you are there anyways.
Test the coil. This is done with an ohm meter testing both sides of the coil. This only insures the windings are good in the coil and not that the spark is getting to the cap consistently. This would normally manifest at all times I believe so it wouldn't explain why only one bank is having an issue but it does rule it out as a possibility. I can not off the top of my head tell you what range the Ohm readings should be but the info is out there and easy to find. Youtube could help with this and I know for a fact Vice Grip Garage (Derek) shows how on most of his video's if you need help there.
Because it is intermittent and not a dead hole a spark tester wont help but is nice to see if you have spark at a cylinder. If you have a dead hole on one cylinder at idle it could help and they are super cheap at Harbor Freight. This is more of an FYI than anything.
IF something deeper in the distributor goes bad I would think it would manifest as a random miss fire and/or a no start condition at times and not just one bank or cylinder issue. Guru's please correct me if I'm wrong anywhere here.
Some PCM's control spark so IF there is an issue with wiring or the PCM itself this can cause a miss fire also. I know in this case the PCM was swapped out with a known good one so I'm just mentioning it here and will add any Guru's info they share on those tests for future readers. I am not sure if the 2.9 has the PCM control spark or has an ignition module as I am not super familiar with this engine's ignition system.
I have run across the issue of runs great at full throttle but misses at lower RPM's but that was a turbo engine and spark related so what I learned in that case won't directly help here.