Per the Service Manual, this is a list of possible causes of P0305 code. It seems you may have addressed most of them. Hopes this helps.

A955) ASD RELAY OUTPUT CIRCUIT
(K38) INJECTOR CONTROL NO.5 CIRCUIT
(K16) COIL CONTROL NO.5 CIRCUIT
SPARK PLUG
IGNITION WIRE
IGNITION COIL
FUEL PUMP INLET STRAINER PLUGGED
RESTRICTED FUEL SUPPLY LINE
FUEL PUMP MODULE
FUEL PRESSURE LEAK DOWN
FUEL INJECTOR
ENGINE MECHANICAL PROBLEM
POWERTRAIN CONTROL MODULE (PCM)

VISUAL INSPECTION
NOTE:Anything that affects the speed of the crankshaft can cause a misfire DTC.
NOTE:When a Misfire is detected for a particular cylinder, the PCM will shut down that cylinder's Injector Control circuit.

1.Visually inspect the engine for any of the following conditions:

• Worn serpentine belt
• Binding Engine-Driven accessories: A/C Compressor, P/S Pump, Water pump.
• Misalignment of the Water pump, P/S Pump and A/C Compressor pulleys
• Corroded PCM power and ground circuits.
• Improper CKP, CMP, MAP and TP Sensor mounting
• Poor connector/terminal to component connection. i.e., CKP sensor, Fuel Injector, Ignition coil, etc.
• Vacuum leaks
• Restricted Air Induction system or Exhaust system.
• Internal engine component failures.

 

What is your coolant gauge at when you see the sputtering? It sounds like the outside temp seems to play a factor. So, a cheap "try" would be to replace your IAT sensor, located on your intake boot before the throttle body. You may want to invest in a OBDII tool that will log data. If you can replicate the problem while logging the important values (TPS, RPM, Veh speed, LTFT, STFT, O2 voltages, Coolant temp, Outside temp, MAP, etc) you may be able to see where the problem lies.

 

New observation...
Lst time I told the forum how I traveled up North with no problems...I had a full tank of gas...upon my retun my tank was less than half a tank and the problems stared again...

Time passed and I replaced the gas cap...work few days fine...this week it's sputtering and hesitates on acceleration. I noticed that when I'm under 1/4 tank or little over I have problems, but if im over half tank I'm 98% good.

Thats why my trip up north on full tank was hesitation free...

What you make of this...?

Thank-you

 

Having problems with missed engine speed and loss power it was finally revealed that i had bad wiring on the passenger from of the vehicle.

One the thoughts was the CATS so took to muffler shop and the ramrodded the driver side and the middle honeycomb filter was obliterated and the muffler had lots debris so I replaced both.

Truck running great no missed engine speeds but then the engine light came on P420 code. I was unable to get emissions done. so I thought change o2 sensors. After 200 miles went back to emissions and the light was off so I thought problem solved the problem so when they hooked my truck up OBD readiness Monitor status sai that the sensors for evap, Catalyst 02 , EGR had not reset.

I took in and they did full diagnostic i just got the call that it is the catalyic convertor and they can replace the whole Y unit (both cats n muffler) for 739.

My question is should replace it all or just get the passenger CAT replaced since I already replaced Driver CAT n muffler?

Thanks in advance

 

FYI the CAT Driver & Muffler were replaced in Feb 15