Without knowing what the "fuel vapor hose" is, I decided to take a break from hunting down vacuum leaks and switch back to checking the ignition system. With the engine running, I started disconnecting and reconnecting the electrical connectors on the COPs one by one, starting on bank 2. On cylinders 5, 7, and 8, when I disconnected the COPs connector, the engine stumbled noticeably before recovering. When I plugged it back in, the idle increased momentarily before recovering. But with (the infamous) cylinder 6, there was no apparent change when I unplugged and replugged the COP connector.
So I removed all 8 COPs and all 8 plugs, checking the gaps of all the plugs. One thing I noticed immediately is that the ceramic insulator around the electrode was white for 7 of the 8 plugs (they are pretty much brand new plugs) but it was a greyish tan on the plug from cylinder 6. I'm not quite sure what this means, as most of the diagnostic photo arrays indicate that grey/tan insulator means normal operation, but these are not worn plugs. (My hunch is that it means it's saturated in gasoline because the cylinder isn't firing.)
Anyway, I placed all the COPs and plugs on a sheet of cardboard with each plug/COP pairing arranged according to where they were in the engine. Then I turned the cardboard around 180 degrees and put them all back in. So the plug/COP that had been in cylinder 1 swapped with the ones that had been in cylinder 8, 2 swapped with 7, 3 swapped with 6, and 4 swapped with 5. I made sure everything was seated properly and that all the COPs were pressed down firmly to ensure that the springs were seated on the plugs.
But when I started the engine, there was no change from before. The idle is still rough, it still throws the P0174 code almost immediately, and I still get the same behavior with cylinder 6, where unplugging the COP connector does not appear to make any noticeable difference in the idle.
So I removed the pins from the connector again to make sure the wires hadn't disconnected from the pins somehow. Then I took the plastic connector off #5 and swapped it onto the #6 wires and vice versa. Still no difference.
Now, I have read that a cylinder not firing can cause a lean code, so I unplugged a COP on bank 1 to watch how the sensors reacted. The bank 1 O2 sensor 2 showed a dramatic dip, but then it came back up to normal levels after the PCM adjusted the ratio. So running a cylinder short on bank 1 doesn't produce the rock-bottom O2 sensor readings I'm getting on bank 2.
I'm about out of ideas here. I bought a vacuum pump/tester to rule things out, which I plan to do tonight. I haven't tried swapping O2 sensors yet because everything I've read is that the downstream O2 sensors are for monitoring only and don't cause the PCM to change running conditions. So a bad downstream O2 sensor shouldn't be causing a rough idle. Also, while a vacuum leak is usually the cause of these kinds of error codes, I cannot understand how a vacuum leak would cause this issue only on bank 2 and not on bank 1. Same goes for EGR/DPFE problems. I don't see how such a problem would affect only one side of the engine but not the other.
I'm running out of ideas here...