What is the variation left to right on the LTFTs? They should be pretty close.

I'd probably start checking some things out...
I'd try to validate the vac reading with a gauge to see if the map is valid.
I'd swap front o2 sensor positions and see if the LTFTs profiles follow the sensor to the other bank.
I think I'd do a leakdown test on the rail to see if any injectors are leaking, but don't know if dodge put a fitting on the rail to make that easy or not.

 

Here are some screenshots of plot of narrowed areas of interest. These may better illustrate B1S2 is not operating properly. (?)
Thoughts, comments ....

 

Seems you want to focus on the rear sensor...
Take out both rear sensors and swap bank 1 into bank 2, and bank 2 into bank 1. Then look at the data to see if the trace follows the sensor or stays on the same bank. If the problem swaps banks (follows the sensor), replace that sensor. If the problem stays on the same bank, start looking at what it may be indicating:
https://www.obd-codes.com/p0137

I'm more interested to understand what is up with that always negative long term fuel trim, but I'll be patient while you work your first code.

 

This evening I did three things.

1. Pulled up the fuel rails and pressurized. Turned key to run and listened for fuel pump. Left it like that for 10 minutes then went looking for evidence of drips from each fuel injector. None found.
2. Swapped positions of B1S2 (suspect) with B2S2.
3. Went for a drive and captured some data.

Results:
- No fuel injectors are leaking, none stuck open
- Truck logged a pending code P0157. B2S2 low voltage. The problem followed the sensor. Can conclude definitively the sensor is shot.
- The initial logs of O2 sensor voltage shows definitively the anomaly followed the sensor to the new location B2S2.

Long Term Fuel Trims.
- at steady state drive the LTFT operate in -2% to -7% range. Sometimes gets to 0%. Never goes above 0, never +ve
- at steady state idle the LTFT settle at -8% to -14%
- on decal the LTFT go -15% and lower
- on hard accel, full throttle, it is a total crap shoot as to which way the LTFT will go.

 

Ok, details... How did you conclude that w/o the use of a pressure gauge on the rail? BTW, looks like Dodge provides a schrader valve on the right side rail on the 5.7 hemi.

Buy NTK (OE).

1. What is the output of the front o2s at full throttle?
2. What vac reading does the pcm report at steady state idle? Also what RPM does the pcm report at steady state idle?
3. Does the LTFT range differ between banks?

 

 

At anything more than about half throttle, the PCM will drop into open loop, and ignore the O2 sensors in any event.

 

With respect to the injectors. Interest in them is exploring if there is a chronic rich condition present - because LTFT are always negative. Two possibilities wrt injectors; a) leaking injector(s), b) overpressure fuel rail. With key-on can hear the fuel pump pressurize the system. Conclude there are no injector sealing problem, no leaks. This is based on the injectors pulled out of the heads, still attached to the rails, fuel rails pressurized, and 10 minute time lapse. Nothing wet, no drips, no gas smell, therefore no leaking injector(s). I do not have a gauge to attached to the fuel rail to check for high pressure, yet. High fuel pressure is TBD.

1. At full throttle. Confirming with HeyYou - evidenced in the catalogs both the STFT and LTFT on both banks goto 0.0% at full throttle.
Through full throttle burst, 2 runs:
Ambient 103 kPa
MAP; 95 kPa,
VAC: 103 - 94 = 9 kPa ( 2.6 inHg)
IAT: 0 degC
ECT: 93-96 degC
rpm 4950-5250
TPS 86%,
B1S1 volt, Run1 0.90-0.94, Run2 0.62-0.90 (this sensor is brand new, NTK)
B1S2 volt. Run1 0.94-0.94, Run2 0.90-0.92
B2S1 volt, Run1 0.12-0.46, Run2 0.78-0.88
B2S2 volt, Run1 0.27-0.48, Run2 0.53-0.90 (this is the faulty sensor location atm, this sensor will be replaced)

2. At idle.
Ambient: 103 kPa
MAP: 34 kPa
VAC: 103 - 34 = 69 kPa ( 20.3 inHg )
TPS: 10%-13%
rpm 680
IAT: -1 degC
ECT: 93 degC
B1S1 volt, 0.45-0.69 (this sensor is brand new, NTK)
STFT1 -2.3% / -0.8%
B1S2 volt. 0.38-0.69
LTFT1 -8.6%
B2S1 volt, 0.33-0.75
STFT2 -1.5% / -0.8%
B2S2 volt, 0.00-0.33 (this is the faulty sensor location atm, this sensor will be replaced)
LTFT2 -8.6%

3. The LTFT range is same/similar between banks. They run fairly close together, generally within 1%. There are intermittent excursions when the faulting sensor acts up. See charts previously posted above.

 

You're such a spoiler, I want him to confirm they show full rich.

 

Thinking your MAP sensor is bad. Should see around 17-21 inHg at idle, and 34kpa converts to 10 inHg. Replace and then recheck closed loop, LTFT should start changing for the better. Report back findings

Recommend you acquire an independent vacuum gauge and a fuel pressure gauge... invaluable, easy, and fast tests... well worth the little they cost on Amazon.