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If you truly have 0 oil pressure, I would stop driving the truck. 0 oil pressure means you have a bearing issue, or oil pump failure, at the least. Also the pressure in your lifters fail and then the valves wont open properly and the engine runs terrible until you build up pressure again, such as revving it.I am assuming you have a hydraulic cam.
Sounds like I'm in the minority here, but I'm not sure the oil pressure would be my focus. It's not good, but you're saying it drops to zero when it stumbles badly and the idle drops very low. If your engine is stumbling and at a very low idle rpm you won't have oil pressure. What's the pressure when its idling properly?