Re: opinion time from everyone.
a gallon of oil being burned in 6 weeks is staggering. you mentioned that you have seen low oil pressure associated which then prompts you to add oil... this indicates that the oil level is low enough that the pump is sucking air. if the oil is this low, you should be adding closer to 6 qts to bring it to the H mark on the dipstick. when does the oil pressure drop? under load or at idle? if it is at idle or very low engine speeds, is there a sort of vibrating humming noise associated with the drop in pressure? if this is the case, the oil pressure relief valve is sticking open and oil pressure is bypassing the pump discharge and not being routed into the engine where it is needed. this valve should only work at higher engine speeds when the oil pressure is higher than required (there's a little plunger in the pump with a calibrated spring holding it shut. when oil pressure exceeds this spring pressure, the plunger opens and oil is bypassed from the discharge side of the pump back to the inlet side). this is common on higher mileage engines where there has been either sludge buildup or trash has gone through the oiling system.
consuming that much oil, your truck should be smoking like a freight train! one thing to keep in mind is that regardless of the actual failure, be prepared to replace catalysts, air fuel ratio sensors, and possibly rear oxygen sensors depending upon the severity of the oil fouling downstream of the exhaust valves.
hope this helps you